Q3: Are there other ways to arrange the data?

Answer: Yes, there are other ways to arrange and represent the data to make it easy to understand. 1. Descending Order: We can arrange the data from the largest value to the smallest value. This would be: 7, 6, 6, 6, 6, 5, 5,..., 3, 3, 3. This is also useful for quickly finding the largest and…

Data Handling and Presentation Class 6 Mathematics NCERT Solutions

Q1Figure it Out (Page 75)

What would you do to find the most popular game among Naresh’s and Navya’s classmates?

Solution

To Find: The most popular game from the given list.

Method: To find the most popular game, we need to organize the collected data. A good way to do this is by creating a frequency distribution table.

List the categories: List all the unique games mentioned by the students.
Use Tally Marks: Go through the list of students and their favourite games one by one. For each student's choice, place a tally mark ('|') next to the corresponding game in the table.
Count the Frequency: After tallying all the choices, count the tally marks for each game to find its frequency (the number of students who chose it).
Identify the Highest Frequency: The game with the highest frequency is the most popular game.

Example Table Format:

Game	Tally Marks	Frequency (No. of Students)
Kabaddi
Hockey
Cricket
...

Q2Figure it Out (Page 75)

What is the most popular game in their class?

Solution

Given: A list of students and their favourite games.

To Find: The most popular game.

Solution: We will create a frequency distribution table to count the number of students who prefer each game.

Kabaddi: Mehnoor, Simran, Ankita, Arsh, Sarah, Anaya. (Total: 6)
Hockey: Jubimon, Imon, Rehana, Leela, Afshan, Gurpreet, Navjot, Ananya. (Total: 8)
Satoliya (Pittu): Nand, Pushkal, Jivika, Jivisha, Hemal. (Total: 5)
Cricket: Yuvraj, Tahira, Keerat, Bhavya, Soumya, Hardik. (Total: 6)
Badminton: Aarna, Densy. (Total: 2)
Football: Kompal, Rajesh, Thara, Debabrata. (Total: 4)

Frequency Table:

Game	Frequency (No. of Students)
Hockey	8
Kabaddi	6
Cricket	6
Satoliya (Pittu)	5
Football	4
Badminton	2

Comparing the frequencies, Hockey has the highest frequency of 8.

Final Answer: The most popular game in their class is Hockey.

Q3Figure it Out (Page 75)

Try to find out the most popular game among your classmates.

Solution

Objective: To find the most popular game among classmates.

Procedure: This is an activity that involves data collection and organization. Here are the steps to follow:

Plan the Survey: Decide on the question you will ask, for example, "What is your favourite game?". You might want to provide a list of options or let classmates answer freely.
Collect Data: Ask each classmate the question and record their answer. You can create a list similar to the one Navya and Naresh made.
Organize Data: Create a frequency distribution table with the names of the games. Use tally marks to record the choices as you go through your list.
Analyze Data: Count the tally marks for each game to find the frequency.
Draw a Conclusion: The game with the highest frequency is the most popular game among your classmates.

Example: Suppose you survey 20 classmates and get the following results:

Cricket: 7 votes
Football: 5 votes
Badminton: 4 votes
Chess: 3 votes
Kabaddi: 1 vote

In this example, the most popular game would be Cricket.

Q4Figure it Out (Page 75)

Pari wants to respond to the questions given below. Put a tick ( ✓ ) for the questions where she needs to carry out data collection and put a cross ( × ) for the questions where she doesn't need to collect data. Discuss your answers in the classroom. a. What is the most popular TV show among her classmates? □ b. When did India get independence? □ c. How much water is getting wasted in her locality? □ d. What is the capital of India? □

Solution

Analysis: Data collection is needed when the answer is not a known fact and depends on surveying or observing a group or situation.

a. What is the most popular TV show among her classmates? To answer this, Pari must ask her classmates about their preferences. This requires a survey. Therefore, data collection is needed.

b. When did India get independence? This is a historical fact (August 15, 1947) that can be found in books or on the internet. It does not require a new survey or observation. Therefore, data collection is not needed.

c. How much water is getting wasted in her locality? To answer this, Pari would need to observe and measure water wastage from leaking taps, overflowing tanks, etc., over a period. This requires observation and measurement. Therefore, data collection is needed.

d. What is the capital of India? This is a geographical fact (New Delhi) that is widely known and can be looked up. It does not require data collection. Therefore, data collection is not needed.

Final Answer: a. ✓ b. × c. ✓ d. ×

Q1Figure it Out (Page 76)

Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: a. How many students chose jalebi? □ b. Barfi was chosen by □ students? c. How many students chose gujiya? □ d. Rasgulla was chosen by □ students? e. How many students chose gulab jamun? □

Solution

Given: A table with sweets and their preferences shown using tally marks.

To Find: The number of students for each sweet.

Method: We need to count the tally marks for each sweet. The symbol '||||' represents a group of 5.

Jalebi: |||| | = 5 + 1 = 6
Gulab jamun: |||| |||| = 5 + 4 = 9
Gujiya: |||| |||| ||| = 5 + 5 + 3 = 13
Barfi: ||| = 3
Rasgulla: |||| || = 5 + 2 = 7

Completed Table:

Sweets	Tally Marks	No. of Students
Jalebi
Gulab jamun
Gujiya
Barfi
Rasgulla

Answers to the questions: a. How many students chose jalebi? 6 b. Barfi was chosen by 3 students? c. How many students chose gujiya? 13 d. Rasgulla was chosen by 7 students? e. How many students chose gulab jamun? 9

Q2Figure it Out (Page 76)

Is the above table sufficient to distribute each type of sweet to the correct student? Explain. If it is not sufficient, what is the alternative?

Solution

Analysis: The table shows the total count of each sweet needed. For example, it tells Shri Nilesh to buy 13 gujiyas. However, it does not record which specific 13 students chose gujiya.

Answer: No, the table is not sufficient to distribute each type of sweet to the correct student.

Explanation: The table provides only the frequency (the total number) of students who prefer each sweet. It is aggregate data. It does not contain individual data, meaning it does not link a specific student to their choice of sweet. When Shri Nilesh brings the sweets, he will know he has 6 jalebis, but he will not know who the 6 students are that want a jalebi.

Alternative: To be able to distribute the sweets to the correct students, Shri Nilesh would need a list that records each student's name along with their chosen sweet. An alternative method would be:

Create a list: Write down the name of each student and the sweet they chose next to their name.
- Example: Rohan - Jalebi, Priya - Gulab jamun, etc.
Group by choice: Reorganize the list by grouping students under their chosen sweet.
- Jalebi: Rohan, Amit, ...
- Gulab jamun: Priya, Sita, ...

Q1Figure it Out (Page 77)

Help her to figure out the following: a. The largest shoe size in the class is ___ . b. The smallest shoe size in the class is _ . c. There are _ students who wear shoe size 5. d. There are ___ students who wear shoe sizes larger than 4.

Solution

Given: A list of shoe sizes arranged in ascending order: 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7

Solution: By observing the ordered list, we can easily find the answers.

a. The largest shoe size in the class is _____ . The last number in the ascending list is the largest. The largest shoe size is 7.

b. The smallest shoe size in the class is _____ . The first number in the ascending list is the smallest. The smallest shoe size is 3.

c. There are _____ students who wear shoe size 5. We count the number of times '5' appears in the list: 5, 5, 5, 5, 5, 5, 5, 5, 5, 5. It appears 10 times. So, there are 10 students.

d. There are _____ students who wear shoe sizes larger than 4. We need to count the students with shoe sizes 5, 6, and 7.

Number of students with size 5 = 10
Number of students with size 6 = 4
Number of students with size 7 = 1 Total students = 10 + 4 + 1 = 15.

Final Answers: a. 7 b. 3 c. 10 d. 15

Q2Figure it Out (Page 77)

How did arranging the data in ascending order help to answer these questions?

Solution

Explanation: Arranging the data in ascending (or descending) order is a way of organizing it that makes it much easier to interpret and analyze. This organized data helps in the following ways:

Finding Minimum and Maximum Values: The smallest value (minimum) is the first number in the list, and the largest value (maximum) is the last. This can be seen at a glance, without having to search through unorganized data.
Counting Frequencies: All identical values are grouped together, which makes it very easy and quick to count how many times a particular value appears (its frequency). For example, all the 5s are together, making them easy to count.
Identifying the Range: The difference between the maximum and minimum values (the range of the data) is easy to calculate.
Answering Comparative Questions: It simplifies answering questions like "how many students have a shoe size larger than 4?" because we only need to look at the part of the list that comes after all the 4s.

Q3Figure it Out (Page 77)

Are there other ways to arrange the data?

Solution

Answer: Yes, there are other ways to arrange and represent the data to make it easy to understand.

Descending Order: We can arrange the data from the largest value to the smallest value. This would be: 7, 6, 6, 6, 6, 5, 5, ... , 3, 3, 3. This is also useful for quickly finding the largest and smallest values.
Frequency Distribution Table: This is a very common and useful method. A table is created to show each unique data value and how many times it occurs (its frequency). This is often done with tally marks first.

Example for the shoe size data:

Shoe Size Tally Marks Frequency
3
4
5
6
7

This table clearly shows the frequency of each shoe size.

Q4Figure it Out (Page 77)

Write the names of a few trees you see around you. When you observe a tree on the way from your home to school (or while walking from one place to another place), record the data and fill in the following table:
Tree No. of Trees
Peepal
Neem
...
...
a. Which tree was found in the greatest number? b. Which tree was found in the smallest number? c. Were there any two trees found in the same numbers?

Tree	No. of Trees
Peepal
Neem
...
...

Solution

Objective: To collect, organize, and analyze data about trees in the local environment.

Procedure: This is an activity. The steps to complete it are:

Preparation: Before you start your walk, prepare a notebook or a sheet with a table. List the names of common trees you expect to see, like Neem, Peepal, Banyan, Mango, etc. Leave space to add new tree names.
Data Collection: While walking from home to school (or another route), carefully observe the trees. Each time you see a tree from your list, put a tally mark next to its name. If you see a tree not on your list, add it and put a tally mark.
Organize Data: After the walk, count the tally marks for each tree to get the total number (frequency) and fill in the final table.

Sample Data and Solution: Let's assume after the walk, the collected data is as follows:

Tree	Tally Marks	No. of Trees
Peepal
Neem
Banyan
Mango
Gulmohar

Answering the questions based on the sample data:

a. Which tree was found in the greatest number? Looking at the table, the Neem tree has the highest number (7).

b. Which tree was found in the smallest number? The Banyan tree has the smallest number (2).

c. Were there any two trees found in the same numbers? In this sample data, no two trees were found in the same number. (If, for example, Mango was also 3, the answer would be 'Yes, Peepal and Mango').

Q5Figure it Out (Page 77)

Take a blank piece of paper and paste any small news item from a newspaper. Each student may use a different article. Now, prepare a table on the piece of paper as given below. Count the number of each of the letters 'c', 'e', ' i ', ' r ', and ' x ' in the words of the news article, and fill in the table.
Letter c e i r x Any other letter of your choice
Number of times found in the news item
a. The letter found the most number of times is _ . b. The letter found the least number of times is _ . c. List the five letters 'c', 'e', 'i', 'r', 'x' in ascending order of frequency. Now, compare the order of your list with that of your classmates. Is your order the same or nearly the same as theirs? (Almost everyone is likely to get the order ' x, c, r, i, e'.) Why do you think this is the case? d. Write the process you followed to complete this task. e. Discuss with your friends the processes they followed. f. If you do this task with another news item, what process would you follow?

Solution

Objective: To collect and analyze frequency data of letters in a text.

Procedure and Sample Solution: This is an activity. Here is a sample execution.

Sample News Item: "The recent cricket match created excitement. Everyone is celebrating the incredible victory."

Data Collection:

Count 'c': recent, cricket, created, incredible. (Count: 5)
Count 'e': the, recent, cricket, created, excitement, everyone, celebrating. (Count: 12)
Count 'i': cricket, excitement, is, celebrating, incredible, victory. (Count: 7)
Count 'r': cricket, created, everyone, celebrating, incredible, victory. (Count: 6)
Count 'x': excitement. (Count: 1)
Let's choose 't' as another letter: the, recent, cricket, created, excitement, celebrating, victory. (Count: 7)

Completed Table:

Letter	c	e	i	r	x	t
Number of times found in the news item	5	12	7	6	1	7

Answering the questions based on sample data:

a. The letter found the most number of times is e .

b. The letter found the least number of times is x .

c. List the five letters 'c', 'e', 'i', 'r', 'x' in ascending order of frequency. Based on our counts (c=5, e=12, i=7, r=6, x=1), the ascending order of frequency is: x (1), c (5), r (6), i (7), e (12). The order of letters is x, c, r, i, e. This matches the expected order. Why is the order similar for everyone? This happens because in the English language, some letters are used far more frequently than others. 'E' is the most common letter, while 'X', 'Q', and 'Z' are among the least common. This pattern holds true for almost any piece of English text.

d. Write the process you followed to complete this task.

Selected and pasted a news article.
Read the article carefully, one letter at a time.
Used tally marks to count the occurrences of each required letter ('c', 'e', 'i', 'r', 'x').
Counted the tally marks to get the final frequency for each letter.
Filled the frequencies into the table.

e. Discuss with your friends the processes they followed. This is a discussion point. Some friends might have scanned the article for one letter at a time, while others might have read word by word, tallying all required letters as they appeared.

f. If you do this task with another news item, what process would you follow? I would follow the same process because it is systematic and helps avoid errors. Reading through the text and using tally marks is an effective way to count frequencies accurately.

Q1Figure it Out (Page 83)

The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori:
Day Number of Books Borrowed
Monday □ □ □
Tuesday □ □
Wednesday □ □ □ □ □
Thursday □
Friday □ □ □ □ □ □
Saturday □ □ □ □ □ □ □
(Note: Each □ represents one book.) a. On which day were the minimum number of books borrowed? b. What was the total number of books borrowed during the week? c. On which day were the maximum number of books borrowed? What may be the possible reason?

Day	Number of Books Borrowed
Monday	□ □ □
Tuesday	□ □
Wednesday	□ □ □ □ □
Thursday	□
Friday	□ □ □ □ □ □
Saturday	□ □ □ □ □ □ □

Solution

Given: A pictograph showing books borrowed each day of a week. The key is 1 symbol (□) = 1 book.

Solution: First, let's count the number of books borrowed each day by counting the symbols.

Monday: 3 symbols = 3 books
Tuesday: 2 symbols = 2 books
Wednesday: 5 symbols = 5 books
Thursday: 1 symbol = 1 book
Friday: 6 symbols = 6 books
Saturday: 7 symbols = 7 books

Now we can answer the questions.

a. On which day were the minimum number of books borrowed? Comparing the daily numbers (3, 2, 5, 1, 6, 7), the smallest number is 1. This occurred on Thursday. Answer: Thursday.

b. What was the total number of books borrowed during the week? We need to add the number of books borrowed each day. Total books = 3 (Mon) + 2 (Tue) + 5 (Wed) + 1 (Thu) + 6 (Fri) + 7 (Sat) = 24 books. Answer: 24 books.

c. On which day were the maximum number of books borrowed? What may be the possible reason? Comparing the daily numbers, the largest number is 7. This occurred on Saturday. Answer: Saturday. Possible Reason: Students might borrow more books on Saturday because they have Sunday (a holiday) ahead of them, giving them more free time to read.

Q2Figure it Out (Page 83)

Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites he sold to these six shopkeepers are given below -
Shopkeeper Number of Kites Sold
Chaman 250
Rani 300
Rukhsana 100
Jasmeet 450
Jetha Lal 250
Poonam Ben 700
Prepare a pictograph using the symbol ⊟ to represent 100 kites. Answer the following questions: a. How many symbols represent the kites that Rani purchased? b. Who purchased the maximum number of kites? c. Who purchased more kites, Jasmeet or Chaman? d. Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?

Shopkeeper	Number of Kites Sold
Chaman	250
Rani	300
Rukhsana	100
Jasmeet	450
Jetha Lal	250
Poonam Ben	700

Solution

Given: Data on kites sold to six shopkeepers. Task: Prepare a pictograph with the key: 1 symbol (⊟) = 100 kites.

Pictograph Preparation: Since 1 symbol = 100 kites, a half symbol will represent

100 \div 2 = 50

kites.

Chaman (250): $250 = 200 + 50$ . So, 2 full symbols and 1 half symbol.
Rani (300): $300 = 3 \times 100$ . So, 3 full symbols.
Rukhsana (100): $100 = 1 \times 100$ . So, 1 full symbol.
Jasmeet (450): $450 = 400 + 50$ . So, 4 full symbols and 1 half symbol.
Jetha Lal (250): $250 = 200 + 50$ . So, 2 full symbols and 1 half symbol.
Poonam Ben (700): $700 = 7 \times 100$ . So, 7 full symbols.

Pictograph:

Shopkeeper	Number of Kites (⊟ = 100 kites)
Chaman	⊟ ⊟ (half ⊟)
Rani	⊟ ⊟ ⊟
Rukhsana	⊟
Jasmeet	⊟ ⊟ ⊟ ⊟ (half ⊟)
Jetha Lal	⊟ ⊟ (half ⊟)
Poonam Ben	⊟ ⊟ ⊟ ⊟ ⊟ ⊟ ⊟

Answering the questions:

a. How many symbols represent the kites that Rani purchased? Rani purchased 300 kites. Since 1 symbol = 100 kites, the number of symbols is

300 \div 100 = 3

. Answer: 3 symbols.

b. Who purchased the maximum number of kites? Looking at the data table, the highest number is 700, which corresponds to Poonam Ben. Answer: Poonam Ben.

c. Who purchased more kites, Jasmeet or Chaman? Jasmeet purchased 450 kites. Chaman purchased 250 kites. Since

450 > 250

, Jasmeet purchased more kites. Answer: Jasmeet.

d. Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?

Kites purchased by Rani = 300.
Double the number of kites Rani purchased = $2 \times 300 = 600$ .
Kites purchased by Poonam Ben = 700. Since $700 > 600$ , Poonam Ben did purchase more than double the number of kites Rani purchased. Answer: Yes, she is correct. Because Poonam Ben purchased 700 kites, which is 100 more than double the 300 kites Rani purchased.

Q1Figure it Out (Page 88)

How many total cars passed through the crossing between 6 a.m. and noon?

Solution

Given: A bar graph showing the number of vehicles passing a crossing at different hours. To Find: The total number of cars that passed between 6 a.m. and noon.

Solution: We need to read the value from the top of each bar for the given time intervals and add them together.

6 a.m. - 7 a.m.: The bar is halfway between 100 and 200, which is approximately 150 vehicles.
7 a.m. - 8 a.m.: The bar reaches 1200. So, 1200 vehicles.
8 a.m. - 9 a.m.: The bar reaches 1000. So, 1000 vehicles.
9 a.m. - 10 a.m.: The bar reaches 800. So, 800 vehicles.
10 a.m. - 11 a.m.: The bar reaches 700. So, 700 vehicles.
11 a.m. - 12 noon: The bar reaches 600. So, 600 vehicles.

Total cars =

150 + 1200 + 1000 + 800 + 700 + 600

Total cars = 4450

Final Answer: A total of 4450 cars passed through the crossing between 6 a.m. and noon.

Q2Figure it Out (Page 88)

Why do you think so little traffic occurred during the hour of 6-7 a.m., as compared to the other hours from 7 a.m.-noon?

Solution

Observation: The bar for 6-7 a.m. is the shortest, indicating the least amount of traffic.

Reasoning: The time between 6 a.m. and 7 a.m. is very early in the morning. At this time:

Most schools and offices have not yet opened.
The majority of people have not started their daily commute to work or school.
Commercial activities are generally low. Therefore, the volume of traffic on the roads is minimal compared to the later morning hours which constitute the peak rush hour.

Q3Figure it Out (Page 88)

Why do you think the traffic was the heaviest between 7-8 a.m.?

Solution

Observation: The bar for 7-8 a.m. is the tallest, indicating the maximum traffic flow.

Reasoning: The time between 7 a.m. and 8 a.m. is typically the start of the morning rush hour. During this period:

People are traveling to their workplaces.
Students are traveling to their schools.
Public transport is at its peak operation. This simultaneous movement of a large number of people results in the heaviest traffic on the roads.

Q4Figure it Out (Page 88)

Why do you think the traffic was lesser and lesser each hour after 8 a.m. all the way until noon?

Solution

Observation: The bars for 8-9 a.m. (1000), 9-10 a.m. (800), 10-11 a.m. (700), and 11 a.m.-12 noon (600) show a decreasing trend.

Reasoning: After the peak morning rush hour (which is typically from 7 a.m. to 9 a.m.), the volume of traffic starts to decrease because:

Most people have already reached their destinations (offices, schools, etc.).
The number of commuters on the road reduces significantly. While there is still traffic for other purposes (shopping, meetings, deliveries), it is not as concentrated as during the morning rush. This leads to a gradual decline in traffic volume as the morning progresses towards noon.

Q1Figure it Out (Page 93-99)

Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected:
Name of Insect Number
Butterflies 10
Honeybees 15
Dragonflies 8
Grasshoppers 12
Help her prepare a bar graph representing this data.

Name of Insect	Number
Butterflies	10
Honeybees	15
Dragonflies	8
Grasshoppers	12

Solution

Objective: To represent the given data using a bar graph.

Steps to create the bar graph:

Draw Axes: Draw a horizontal line (x-axis) and a vertical line (y-axis).
Label Axes: Label the horizontal axis as 'Name of Insect' and the vertical axis as 'Number of Insects'.
Choose a Scale: The numbers are 10, 15, 8, 12. A suitable scale for the vertical axis would be 1 unit length = 2 insects. Mark the vertical axis at equal intervals: 0, 2, 4, 6, 8, 10, 12, 14, 16.
Mark Categories: On the horizontal axis, mark the names of the insects (Butterflies, Honeybees, Dragonflies, Grasshoppers) at equal distances.
Draw Bars: For each insect, draw a vertical bar of uniform width. The height of the bar will correspond to the number of insects, based on the chosen scale.
- Butterflies (10): The height will be up to the '10' mark on the vertical axis.
- Honeybees (15): The height will be halfway between the '14' and '16' marks.
- Dragonflies (8): The height will be up to the '8' mark.
- Grasshoppers (12): The height will be up to the '12' mark.
Title the Graph: Give the graph a suitable title, such as 'Insects Seen in a Tea Garden'.

Description of the resulting Bar Graph: The bar graph will have four vertical bars. The bar for Honeybees will be the tallest, followed by Grasshoppers, then Butterflies, and the bar for Dragonflies will be the shortest.

Q2Figure it Out (Page 93-99)

Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a two-hour period.
City Number of tickets
Vidisha 24
Jabalpur 20
Seoni 16
Indore 28
Sagar 16
She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph. a. Write the number of tickets sold for Vidisha above the bar. b. Write the number of tickets sold for Jabalpur above the bar. c. The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph? d. Draw the correct bar for Sagar. e. Add the scale of the bar graph by placing the correct numbers on the vertical axis. f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).

City	Number of tickets
Vidisha	24
Jabalpur	20
Seoni	16
Indore	28
Sagar	16

Solution

Given: Data on ticket sales and an incomplete bar graph.

Solution:

a. Write the number of tickets sold for Vidisha above the bar. From the table, 24 tickets were sold for Vidisha. So, we write '24' above the bar for Vidisha.

b. Write the number of tickets sold for Jabalpur above the bar. From the table, 20 tickets were sold for Jabalpur. So, we write '20' above the bar for Jabalpur.

c. The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?

For Vidisha: 6 units represent 24 tickets. So, 1 unit = $24 \div 6 = 4$ tickets.
For Jabalpur: 5 units represent 20 tickets. So, 1 unit = $20 \div 5 = 4$ tickets. The scale for this graph is 1 unit length = 4 tickets.

d. Draw the correct bar for Sagar. Number of tickets for Sagar = 16. Height of the bar in units = Total tickets / Scale =

16 \div 4 = 4

units. So, we draw a bar for Sagar with a height of 4 units.

e. Add the scale of the bar graph by placing the correct numbers on the vertical axis. Since 1 unit = 4 tickets, the vertical axis should be marked at equal intervals as: 0, 4, 8, 12, 16, 20, 24, 28, ...

f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).

Seoni: Number of tickets = 16. The height of the bar should be $16 \div 4 = 4$ units. The bar in the graph is 4 units high. So, the bar for Seoni is correct.
Indore: Number of tickets = 28. The height of the bar should be $28 \div 4 = 7$ units. The bar in the graph is shown as 6 units high. So, the bar for Indore is incorrect. The correct bar should be drawn with a height of 7 units.

Q3Figure it Out (Page 93-99)

Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.:
bike car bike bus bike bike
bike auto rickshaw bicycle bullock cart bicycle auto rickshaw
car scooter car auto rickshaw bicycle bike
car auto rickshaw bike scooter bike car
bicycle scooter bicycle scooter bike bus
auto rickshaw auto rickshaw bike bicycle bus bike
bicycle scooter bus scooter auto rickshaw bike
scooter bicycle bike bullock cart auto rickshaw scooter
car scooter
a. Prepare a frequency distribution table for the data. b. Which means of transport was used the most? c. If you were there to collect this data, how could you do it? Write the steps or process.

bike	car	bike	bus	bike	bike
bike	auto rickshaw	bicycle	bullock cart	bicycle	auto rickshaw
car	scooter	car	auto rickshaw	bicycle	bike
car	auto rickshaw	bike	scooter	bike	car
bicycle	scooter	bicycle	scooter	bike	bus
auto rickshaw	auto rickshaw	bike	bicycle	bus	bike
bicycle	scooter	bus	scooter	auto rickshaw	bike
scooter	bicycle	bike	bullock cart	auto rickshaw	scooter
car	scooter

Solution

Given: A list of vehicles observed over one hour.

a. Prepare a frequency distribution table for the data. We will count the occurrences of each type of vehicle using tally marks.

Means of Transport	Tally Marks	Frequency (Number)
Bike
Car
Bus
Auto Rickshaw
Bicycle
Scooter
Bullock Cart

b. Which means of transport was used the most? By looking at the frequency column in the table, the highest frequency is 13, which corresponds to the Bike. Final Answer: Bike was used the most.

c. If you were there to collect this data, how could you do it? Write the steps or process. Here is a systematic process to collect this data:

Preparation: Prepare a sheet with a table listing the expected means of transport (Bike, Car, Bus, etc.) in one column and a second column for Tally Marks.
Observation: Stand at the observation point (in front of the house) from 9 a.m. to 10 a.m.
Recording: Every time a vehicle passes, make a tally mark ('|') in the row corresponding to that vehicle type. If a new type of vehicle appears, add it to the list and make a tally mark.
Grouping: For every fifth mark, draw a diagonal line across the previous four (||||) to make counting easier.
Final Count: After the observation period is over, count the total tally marks for each vehicle type to get the final frequency. This method is efficient and reduces the chances of miscounting.

Q4Figure it Out (Page 93-99)

Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared: a. The minimum number of times. b. The maximum number of times. c. Find numbers that appeared an equal number of times.

Solution

Objective: To perform an experiment, collect data, and analyze it.

Procedure: This is an activity. The results will vary for each person who performs it. Here is a sample result of rolling a die 30 times.

Sample Data (Results of 30 rolls): 4, 1, 6, 5, 2, 3, 5, 4, 1, 6, 2, 5, 3, 4, 6, 1, 5, 2, 4, 5, 6, 3, 2, 1, 5, 4, 6, 2, 3, 4

Frequency Distribution Table:

Number on Die	Tally Marks	Frequency
1
2
3
4
5
6

Analysis of Sample Data:

a. The minimum number of times. Looking at the frequency column (4, 5, 4, 6, 6, 5), the minimum frequency is 4. This occurred for the numbers 1 and 3. Answer (for this sample): The numbers 1 and 3 appeared the minimum number of times (4 times each).

b. The maximum number of times. The maximum frequency is 6. This occurred for the numbers 4 and 5. Answer (for this sample): The numbers 4 and 5 appeared the maximum number of times (6 times each).

c. Find numbers that appeared an equal number of times.

Numbers 1 and 3 both appeared 4 times.
Numbers 2 and 6 both appeared 5 times.
Numbers 4 and 5 both appeared 6 times. Answer (for this sample): The pairs (1, 3), (2, 6), and (4, 5) appeared an equal number of times.

Q5Figure it Out (Page 93-99)

Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches:
Wickets Taken Number of Matches
0 2
1 4
2 6
3 8
4 3
5 5
6 1
7 1
a. What information is this table giving? b. What may be the title of this table? c. What caught your attention in this table? d. In how many matches has Bumrah taken 4 wickets? e. Mayank says, "If we want to know the total number of wickets he has taken in his last 30 matches, we have to add the numbers 0, 1, 2, 3 ..., up to 7." Can Mayank get the total number of wickets taken in this way? Why? f. How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?

Wickets Taken	Number of Matches
0	2
1	4
2	6
3	8
4	3
5	5
6	1
7	1

Solution

Given: A frequency table of wickets taken by a bowler.

a. What information is this table giving? This table shows the performance of the bowler Jaspreet Bumrah over his last 30 matches. It tells us the frequency, i.e., in how many matches he took a specific number of wickets (from 0 to 7).

b. What may be the title of this table? A suitable title would be: "Performance of Jaspreet Bumrah: Wickets Taken in the Last 30 Matches".

c. What caught your attention in this table? (This answer can be subjective.) One interesting point is that he most frequently took 3 wickets in a match (in 8 matches). Another point is that he had a very successful performance of taking 7 wickets in one match.

d. In how many matches has Bumrah taken 4 wickets? Looking at the row for '4' wickets taken, the corresponding number of matches is 3. Answer: Bumrah has taken 4 wickets in 3 matches.

e. Can Mayank get the total number of wickets taken in this way? Why? No, Mayank's method is incorrect. Adding

0+1+2+3+4+5+6+7

just sums up the categories of wickets. It does not account for how many times each event occurred. For example, he took 3 wickets in 8 different matches, so those 8 matches contribute

3 \times 8 = 24

wickets to the total, not just 3.

f. How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table? To find the total number of wickets, you must multiply the number of wickets taken in each category by the number of matches in which that occurred, and then sum up all these products.

Calculation:

0 wickets in 2 matches = $0 \times 2 = 0$
1 wicket in 4 matches = $1 \times 4 = 4$
2 wickets in 6 matches = $2 \times 6 = 12$
3 wickets in 8 matches = $3 \times 8 = 24$
4 wickets in 3 matches = $4 \times 3 = 12$
5 wickets in 5 matches = $5 \times 5 = 25$
6 wickets in 1 match = $6 \times 1 = 6$
7 wickets in 1 match = $7 \times 1 = 7$

Total Wickets =

0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90

Final Answer: The total number of wickets taken by Bumrah in his last 30 matches is 90.

Q6Figure it Out (Page 93-99)

The following pictograph shows the number of tractors in five different villages.
Villages Number of Tractors
Village A 🚜 🚜 🚜 🚜 🚜 🚜
Village B 🚜 🚜 🚜 🚜 🚜
Village C 🚜 🚜 🚜 🚜 🚜 🚜 🚜 🚜
Village D 🚜 🚜 🚜
Village E 🚜 🚜 🚜 🚜 🚜 🚜
(Note: Each 🚜 symbol represents 1 tractor.) Observe the pictograph and answer the following questions- a. Which village has the smallest number of tractors? b. Which village has the most tractors? c. How many more tractors does Village C have than Village B? d. Komal says, "Village D has half the number of tractors as Village E." Is she right?

Villages	Number of Tractors
Village A	🚜 🚜 🚜 🚜 🚜 🚜
Village B	🚜 🚜 🚜 🚜 🚜
Village C	🚜 🚜 🚜 🚜 🚜 🚜 🚜 🚜
Village D	🚜 🚜 🚜
Village E	🚜 🚜 🚜 🚜 🚜 🚜

Solution

Given: A pictograph showing the number of tractors in five villages. Key: 1 symbol (🚜) = 1 tractor.

Solution: First, let's count the number of tractors in each village.

Village A: 6 symbols = 6 tractors
Village B: 5 symbols = 5 tractors
Village C: 8 symbols = 8 tractors
Village D: 3 symbols = 3 tractors
Village E: 6 symbols = 6 tractors

a. Which village has the smallest number of tractors? Comparing the numbers (6, 5, 8, 3, 6), the smallest is 3, which corresponds to Village D. Answer: Village D.

b. Which village has the most tractors? The largest number is 8, which corresponds to Village C. Answer: Village C.

c. How many more tractors does Village C have than Village B?

Number of tractors in Village C = 8
Number of tractors in Village B = 5
Difference = $8 - 5 = 3$ Answer: Village C has 3 more tractors than Village B.

d. Komal says, "Village D has half the number of tractors as Village E." Is she right?

Number of tractors in Village D = 3
Number of tractors in Village E = 6
Half the number of tractors in Village E = $6 \div 2 = 3$ . Since the number of tractors in Village D (3) is equal to half the number of tractors in Village E (3), Komal is right. Answer: Yes, she is right.

Q7Figure it Out (Page 93-99)

The number of girl students in each class of a school is depicted by the pictograph:
Classes Number of Girl Students
1 👧👧👧👧👧👧
2 👧👧👧👧(half 👧)
3 👧👧👧👧👧
4 👧👧👧(half 👧)
5 👧👧(half 👧)
6 👧👧👧👧
7 👧👧👧
8 👧(half 👧)
(Note: Assume 1 full symbol 👧 represents 4 girls.) Observe this pictograph and answer the following questions: a. Which class has the least number of girl students? b. What is the difference between the number of girls in Class 5 and 6? c. If two more girls were admitted in Class 2, how would the graph change? d. How many girls are there in Class 7?

Classes	Number of Girl Students
1	👧👧👧👧👧👧
2	👧👧👧👧(half 👧)
3	👧👧👧👧👧
4	👧👧👧(half 👧)
5	👧👧(half 👧)
6	👧👧👧👧
7	👧👧👧
8	👧(half 👧)

Solution

Given: A pictograph showing the number of girl students. Key: 1 full symbol (👧) = 4 girls. This means a half symbol =

4 \div 2 = 2

girls.

Solution: First, let's calculate the number of girls in each class.

Class 1: 6 full symbols = $6 \times 4 = 24$ girls
Class 2: 4.5 symbols = $(4 \times 4) + 2 = 18$ girls
Class 3: 5 full symbols = $5 \times 4 = 20$ girls
Class 4: 3.5 symbols = $(3 \times 4) + 2 = 14$ girls
Class 5: 2.5 symbols = $(2 \times 4) + 2 = 10$ girls
Class 6: 4 full symbols = $4 \times 4 = 16$ girls
Class 7: 3 full symbols = $3 \times 4 = 12$ girls
Class 8: 1.5 symbols = $(1 \times 4) + 2 = 6$ girls

a. Which class has the least number of girl students? Comparing the numbers, the smallest is 6, which corresponds to Class 8. Answer: Class 8.

b. What is the difference between the number of girls in Class 5 and 6?

Number of girls in Class 6 = 16
Number of girls in Class 5 = 10
Difference = $16 - 10 = 6$ Answer: The difference is 6 girls.

c. If 2 more girls were admitted in Class 2, how would the graph change?

Current number of girls in Class 2 = 18.
New number of girls = $18 + 2 = 20$ .
To represent 20 girls, we need $20 \div 4 = 5$ full symbols. Answer: The graph for Class 2 would change from 4 full symbols and one half symbol to 5 full symbols.

d. How many girls are there in Class 7? Class 7 has 3 full symbols. Number of girls =

3 \times 4 = 12

. Answer: There are 12 girls in Class 7.

Q8Figure it Out (Page 93-99)

Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka's Bagalkote and Vijaypura districts. The government took an initiative to protect this breed by providing support to those who adopted these dogs. Due to this initiative, the number of these dogs increased. The number of Mudhol dogs in six villages of Karnataka are as follows- Village A : 18, Village B : 36, Village C : 12, Village D : 48, Village E : 18, Village F : 24 Prepare a pictograph and answer the following questions: a. What will be a useful scale or key to draw this pictograph? b. How many symbols will you use to represent the dogs in Village B? c. Kamini said that the number of these dogs in Village B and Village D together will be more than the number of these dogs in the other 4 villages. Is she right? Give reasons for your response.

Solution

Given Data:

Village A: 18, Village B: 36, Village C: 12, Village D: 48, Village E: 18, Village F: 24

a. What will be a useful scale or key to draw this pictograph? All the given numbers (18, 36, 12, 48, 18, 24) are multiples of 6. Therefore, a useful scale would be 1 symbol = 6 dogs.

Pictograph (using the key: 🐕 = 6 dogs):

Village A (18): $18 \div 6 = 3$ symbols (🐕🐕🐕)
Village B (36): $36 \div 6 = 6$ symbols (🐕🐕🐕🐕🐕🐕)
Village C (12): $12 \div 6 = 2$ symbols (🐕🐕)
Village D (48): $48 \div 6 = 8$ symbols (🐕🐕🐕🐕🐕🐕🐕🐕)
Village E (18): $18 \div 6 = 3$ symbols (🐕🐕🐕)
Village F (24): $24 \div 6 = 4$ symbols (🐕🐕🐕🐕)

Final Pictograph Table:

Village	Number of Mudhol Hounds (🐕 = 6 dogs)
Village A	🐕🐕🐕
Village B	🐕🐕🐕🐕🐕🐕
Village C	🐕🐕
Village D	🐕🐕🐕🐕🐕🐕🐕🐕
Village E	🐕🐕🐕
Village F	🐕🐕🐕🐕

b. How many symbols will you use to represent the dogs in Village B? Village B has 36 dogs. Using the scale of 1 symbol = 6 dogs, we need

36 \div 6 = 6

symbols. Answer: 6 symbols.

c. Kamini said that the number of dogs in Village B and Village D together will be more than the number of dogs in the other 4 villages. Is she right? Give reasons for your response.

Step 1: Calculate the total number of dogs in Village B and Village D. Total = $36 + 48 = 84$ dogs.
Step 2: Calculate the total number of dogs in the other 4 villages (A, C, E, F). Total = $18 + 12 + 18 + 24 = 72$ dogs.
Step 3: Compare the two totals. $84 > 72$ .

Answer: Yes, Kamini is right. The total number of dogs in villages B and D is 84, which is greater than the total number of dogs in the other four villages, which is 72.

Q9Figure it Out (Page 93-99)

A survey of 120 school students was conducted to find out which activity they preferred to do in their free time:
Preferred Activity Number of Students
Playing 45
Reading story books 30
Watching TV 20
Listening to music 10
Painting 15
Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?

Preferred Activity	Number of Students
Playing	45
Reading story books	30
Watching TV	20
Listening to music	10
Painting	15

Solution

Objective: To draw a bar graph for the given data and identify the second most preferred activity.

Bar Graph Construction:

Axes and Labels: Draw and label a horizontal axis ('Preferred Activity') and a vertical axis ('Number of Students').
Scale: Use the given scale: 1 unit length = 5 students. Mark the vertical axis at equal intervals: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45.
Categories: Mark the activities (Playing, Reading, Watching TV, Listening to music, Painting) on the horizontal axis with equal spacing.
Bar Heights: Calculate the height of each bar in units.
- Playing: $45 \div 5 = 9$ units
- Reading story books: $30 \div 5 = 6$ units
- Watching TV: $20 \div 5 = 4$ units
- Listening to music: $10 \div 5 = 2$ units
- Painting: $15 \div 5 = 3$ units
Draw Bars: Draw vertical bars of uniform width for each activity corresponding to the calculated heights.
Title: Add a title, e.g., "Preferred Free Time Activities of Students".

Answering the question: To find the activity preferred by most students other than playing, we look for the second-highest number in the table.

Playing: 45 (Highest)
Reading story books: 30 (Second highest)
Watching TV: 20
Listening to music: 10
Painting: 15

Final Answer: Other than playing, Reading story books is preferred by most students.

Q10Figure it Out (Page 93-99)

Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. Details of the saplings they planted are as follows - (A bar graph is shown with days of the week on the x-axis and number of saplings on the y-axis) a. The total number of saplings planted on Wednesday and Thursday is ___ . b. The total number of saplings planted during the whole week is _ . c. The greatest number of saplings were planted on _ and the least number of saplings were planted on ___ . Why do you think that is the case? Why were more saplings planted on certain days of the week and less on others? Can you think of possible explanations or reasons? How could you try and figure out whether your explanations are correct?

Solution

Given: A bar graph showing the number of saplings planted each day of a week.

Reading the Bar Graph:

Monday: 40 saplings
Tuesday: 60 saplings
Wednesday: 30 saplings
Thursday: 40 saplings
Friday: 80 saplings
Saturday: 60 saplings

a. The total number of saplings planted on Wednesday and Thursday is _____ . Total = Saplings on Wednesday + Saplings on Thursday =

30 + 40 = 70

. Answer: 70.

b. The total number of saplings planted during the whole week is _____ . Total =

40 + 60 + 30 + 40 + 80 + 60 = 310

. Answer: 310.

c. The greatest number of saplings were planted on _____ and the least number of saplings were planted on _____ . Why do you think that is the case?

Greatest: The tallest bar is for Friday, with 80 saplings.
Least: The shortest bar is for Wednesday, with 30 saplings. Answer: The greatest number of saplings were planted on Friday and the least number of saplings were planted on Wednesday.

Possible Explanations/Reasons:

More saplings on Friday/Saturday: More volunteers (students or community members) might be available on these days as it is the end of the school/work week.
Less saplings on Wednesday: There might have been an event like a school test, bad weather (heavy rain), or fewer volunteers available on that particular day.

How to figure out if explanations are correct: To verify the reasons, one could:

Check the school's timetable for that week to see if there were any special events or exams on Wednesday.
Check the weather report for that week to see if it rained on Wednesday.
Ask the teachers or students who participated to find out why the number of volunteers or the time spent planting varied on different days.

Q11Figure it Out (Page 93-99)

The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in fouryear intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?
Year Number of Tigers (approx.)
2006 1400
2010 1700
2014 2200
2018 3000
2022 3700
(A bar graph is shown with these years and their corresponding tiger numbers, but with incorrect bar heights.)

Year	Number of Tigers (approx.)
2006	1400
2010	1700
2014	2200
2018	3000
2022	3700

Solution

Given: A table of the tiger population in India for different years and a bar graph that contains errors.

Analysis of Mistakes: We need to compare the correct data from the table with the heights of the bars shown in the graph.

Year 2006:
- Correct Value (from table): 1400 tigers.
- Value on Graph: The bar for 2006 is shown at the 1000 mark.
- Mistake: The bar is too short. It should be drawn up to 1400 (just below the 1500 line).
Year 2010:
- Correct Value (from table): 1700 tigers.
- Value on Graph: The bar for 2010 is shown at the 2000 mark.
- Mistake: The bar is too tall. It should be drawn up to 1700 (between the 1500 and 2000 lines).
Year 2014:
- Correct Value (from table): 2200 tigers.
- Value on Graph: The bar for 2014 is shown at the 2500 mark.
- Mistake: The bar is too tall. It should be drawn up to 2200 (just above the 2000 line).
Year 2018:
- Correct Value (from table): 3000 tigers.
- Value on Graph: The bar for 2018 is shown at the 2000 mark.
- Mistake: The bar is too short. It should be drawn up to the 3000 mark.
Year 2022:
- Correct Value (from table): 3700 tigers.
- Value on Graph: The bar for 2022 is shown at the 3500 mark.
- Mistake: The bar is too short. It should be drawn up to 3700 (between the 3500 and 4000 lines).

How to Fix the Graph: To fix the graph, each bar needs to be redrawn to the correct height corresponding to the number of tigers for that year from the table, using the scale on the vertical axis.

Q1Figure it Out (Page 103)

If you wanted to visually represent the data of the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars? Why?

Solution

Answer: I would use a graph with vertical bars (also called a column graph).

Reasoning: Height is a vertical measurement—we measure it upwards from the ground. Using vertical bars to represent height is more intuitive and visually suggestive. The audience can immediately associate the upward length of the bars with the concept of 'height'. A taller bar would naturally represent a taller person. While a horizontal bar graph would still be technically correct, it would not be as effective in conveying the information at a glance.

Q2Figure it Out (Page 103)

If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a bar graph with vertical bars or with horizontal bars? Why? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the longest rivers?

Solution

Answer: I would prefer to use a bar graph with horizontal bars.

Reasoning: The length of a river is a horizontal distance measured across the land. Using horizontal bars to represent these lengths is more intuitive. A longer bar would naturally correspond to a longer river, and the horizontal orientation matches the real-world concept of a river's flow across a continent.

Activity: Finding Data and Making a Bar Graph

Step 1: Find the Information (Sample Data) Here is a table of the longest river on each continent:

Continent	Longest River	Length (approx. in km)
Africa	Nile	6650
South America	Amazon	6400
Asia	Yangtze	6300
North America	Mississippi-Missouri	6275
Europe	Volga	3690
Australia	Murray-Darling	3672
Antarctica	Onyx	32

Step 2: Make the Bar Graph

Axes: Draw a horizontal axis (for Length in km) and a vertical axis (for Continent/River).
Scale: Choose a scale for the horizontal axis, e.g., 1 unit = 1000 km. Mark it as 0, 1000, 2000, etc.
Categories: List the continents or river names along the vertical axis.
Draw Bars: Draw horizontal bars for each river, with the length of the bar corresponding to the river's length on the scale.

Which continents have the longest rivers? Based on the data, Africa (Nile), South America (Amazon), Asia (Yangtze), and North America (Mississippi-Missouri) have the longest rivers, all with lengths over 6000 km.

Data Handling and PresentationClass 6 Mathematics NCERT Solutions

What would you do to find the most popular game among Naresh’s and Navya’s classmates?

Solution

What is the most popular game in their class?

Solution

Try to find out the most popular game among your classmates.

Solution

Solution

Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: a. How many students chose jalebi? □ b. Barfi was chosen by □ students? c. How many students chose gujiya? □ d. Rasgulla was chosen by □ students? e. How many students chose gulab jamun? □

Solution

Is the above table sufficient to distribute each type of sweet to the correct student? Explain. If it is not sufficient, what is the alternative?

Solution

Help her to figure out the following: a. The largest shoe size in the class is _____ . b. The smallest shoe size in the class is _____ . c. There are _____ students who wear shoe size 5. d. There are _____ students who wear shoe sizes larger than 4.

Solution

How did arranging the data in ascending order help to answer these questions?

Solution

Are there other ways to arrange the data?

Solution

Solution

Solution

Solution

Solution

How many total cars passed through the crossing between 6 a.m. and noon?

Solution

Why do you think so little traffic occurred during the hour of 6-7 a.m., as compared to the other hours from 7 a.m.-noon?

Solution

Why do you think the traffic was the heaviest between 7-8 a.m.?

Solution

Why do you think the traffic was lesser and lesser each hour after 8 a.m. all the way until noon?

Solution

Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected: Name of InsectNumberButterflies10Honeybees15Dragonflies8Grasshoppers12 Help her prepare a bar graph representing this data.

Solution

Solution

Solution

Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared: a. The minimum number of times. b. The maximum number of times. c. Find numbers that appeared an equal number of times.

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

If you wanted to visually represent the data of the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars? Why?

Solution

If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a bar graph with vertical bars or with horizontal bars? Why? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the longest rivers?

Solution

Help her to figure out the following: a. The largest shoe size in the class is ___ . b. The smallest shoe size in the class is _ . c. There are _ students who wear shoe size 5. d. There are ___ students who wear shoe sizes larger than 4.

Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected:
Name of Insect Number
Butterflies 10
Honeybees 15
Dragonflies 8
Grasshoppers 12
Help her prepare a bar graph representing this data.