Practice Questions

Define the term 'data' as used in mathematics.

A student wants to show the percentage breakdown of their monthly pocket money expenses on food, stationery, and entertainment. Justify why a pie chart is the most appropriate graph for this data.

Analyze the following data set representing the daily temperatures in Celsius for a week and find its range: 25, 28, 22, 31, 26, 24, 29.

List three examples of information that can be collected as data in a school environment.

List the possible outcomes when a standard six-sided die is thrown once.

Explain the purpose of a bar graph.

What is a pictograph?

Create a dataset for the favorite subjects of 40 students where Mathematics is the most popular, and the central angle for the "Science" sector in a pie chart would be $72^\circ$.

A friend claims, "I flipped a coin three times and got heads each time. The next flip is more likely to be tails to balance it out." Evaluate this statement.

In a pie chart representing the favorite sports of students, 35% of the students chose cricket. Calculate the central angle of the sector representing cricket.

A standard six-sided die is rolled once. Calculate the probability of getting a number that is a multiple of 3.

Identify another name for a circle graph.

The number of students in different clubs in a school is given below. Draw a bar graph to represent this data. Choose an appropriate scale.

Design a simple game for two players using a standard six-sided die where Player A has a higher probability of winning than Player B. Justify the probabilities.

The time spent by a student on different activities in a 24-hour day is given: School (6 hours), Sleep (8 hours), Homework (4 hours), Play (3 hours), Others (3 hours). Create a table showing the fraction of the day and the central angle for each activity required to draw a pie chart.

Formulate a real-world scenario and create a hypothetical dataset that would be best represented by a double bar graph. Justify your choice of graph.

The following data shows the number of students in a school who prefer different modes of transport: Bus (180), Car (60), Walk (90), Cycle (30). Total students = 360. A student represents this data using both a bar graph and a pie chart. Critique both representations. Evaluate which graph is better for answering: (a) "How many more students use the bus than walk?" (b) "What proportion of students use a car?" Justify your reasoning.

A pie chart is used to show the monthly budget of a family. If the sector representing 'Food' has a central angle of $90^\circ$, what fraction of the total budget is spent on food?

A box contains 5 red pens, 3 blue pens, and 2 green pens. If one pen is drawn at random, what is the probability that it is not blue?

What is a random experiment?

Describe what 'equally likely outcomes' means in the context of probability. Provide an example.

Critique the use of a pictograph where one symbol represents 1,257 people.

Propose a method to collect data to determine the most popular sport among all students in your school.

Explain the formula for calculating the probability of an event.

The following table shows the number of hours a student spends on different activities during a school day (24 hours). Explain how you would find the central angle for each activity to create a pie chart.

A bag contains 5 red balls, 3 blue balls, and 2 green balls. Without looking, a ball is drawn. List all possible outcomes and state the total number of outcomes.

Describe the step-by-step process of converting a data table into a pie chart. Use the concept of central angles in your explanation.

The weights (in kg) of 20 students in a class are given below. Organize this data into a frequency distribution table using class intervals 30-35, 35-40, and so on (where 35 is included in the 35-40 interval). 40, 38, 33, 48, 52, 38, 43, 55, 46, 39, 41, 47, 58, 35, 37, 49, 53, 44, 42, 36

A survey was conducted to find out the preferred brand of toothpaste among 180 people. The results are shown below. Calculate the central angle for each brand and construct a pie chart to represent this data.

Two coins are tossed simultaneously. Calculate the probability of getting: (a) Exactly one head. (b) At least one head.

A bar graph shows that the production of wheat in a farm was 400 quintals in 2020 and 500 quintals in 2021. Compare the production in 2020 to 2021 by expressing it as a simplified ratio.

The monthly budget of a family is shown in a pie chart. The sector for 'Rent' has a central angle of $72^\circ$. If the total monthly income of the family is ₹30,000, calculate the amount spent on rent.

From a well-shuffled deck of 52 playing cards, one card is drawn at random. Calculate the probability of drawing: (a) A king (b) A spade (c) A red ace

The following data shows the marks obtained by a student in Term 1 and Term 2 examinations (out of 100). Analyze the data to answer the questions.

(a) In which subject did the student improve the most? (b) In which subject did the performance decline? (c) Compare the total marks in Term 1 and Term 2.

You have data on the number of cars sold by five different companies in a year. Justify why a bar graph is a better choice than a line graph to represent this data.

A bar graph shows the profits of Company X from 2020 to 2023. The profits are: 2020 (₹10 Crores), 2021 (₹12 Crores), 2022 (₹11 Crores), 2023 (₹14 Crores). The company report states, "Our profits have consistently increased every year." Evaluate the validity of this statement based on the data.

Formulate a problem involving a bag of different colored marbles where the probability of drawing a blue marble is $\frac{1}{4}$ and the probability of drawing a red marble is $\frac{1}{3}$. Determine the minimum number of marbles in the bag and the composition of marbles by color.

What is the primary function of a double bar graph? Describe a scenario where it would be useful.

Formulate a survey question to find out the preferred online learning platform among students (e.g., YouTube, Khan Academy, BYJU'S, Other). Create a hypothetical dataset for a survey of 200 students. Justify the choice of a pie chart to display this data and calculate the central angles for your dataset.

Explain the key differences between a pictograph, a bar graph, and a circle graph. Describe what kind of information each graph is best at representing.

Design an experiment to test if a six-sided die is fair. Describe the steps you would take to collect data, how you would represent the data, and formulate a criterion to evaluate the die's fairness.

A survey of 100 people about their favorite fruit shows: Apples (40), Bananas (30), Oranges (20), Grapes (10). A student creates a pie chart where the central angles are: Apples ($150^\circ$), Bananas ($100^\circ$), Oranges ($80^\circ$), Grapes ($30^\circ$). Critique the student's work and propose the correct central angles.

The sales of two competing electronics stores (Store X and Store Y) over 4 months are given in the table (in thousands of ₹).

(a) Represent this data using a double bar graph. (b) In which month was the combined sale from both stores the highest? (c) What is the difference in the total sales of the two stores over the 4 months?

Slips of paper marked with numbers from 1 to 25 are placed in a box and mixed thoroughly. One slip is drawn at random. Analyze the possible outcomes and calculate the probability of drawing: (a) An even number. (b) A number which is a perfect square. (c) A prime number less than 15. (d) A number divisible by both 2 and 3.

A pie chart shows the distribution of nutrients in a health drink. The angle for Protein is $90^\circ$, Carbohydrates is $144^\circ$, and the rest is Fats. If the total weight of the pack is 250 grams, calculate the weight of Fats in grams.