Practice Questions

Identify which of the following is a statistical question: (a) What is your favorite color? (b) How many hours do students in your class sleep on average?

Based on the provided bar graph showing monthly sales for a company, answer the following: (a) In which month were the sales the highest, and what was the approximate sales value? (b) Calculate the total sales for the first quarter (Jan, Feb, Mar). (c) Compare the sales of May and June. (A bar graph would be provided in an actual test. For this problem, assume the following values: Jan=30k, Feb=45k, Mar=40k, Apr=50k, May=60k, June=55k).

Define Arithmetic Mean.

Find the median of the following scores from a math test: $15, 23, 18, 12, 25, 18, 20$.

A company's employee salaries are: ₹20,000, ₹22,000, ₹25,000, ₹28,000, and ₹1,50,000 per month. Justify which measure of central tendency, mean or median, would be more appropriate to represent a 'typical' salary.

The daily temperatures recorded in a city for a week were $25^\circ\text{C}, 27^\circ\text{C}, 24^\circ\text{C}, 28^\circ\text{C}, 30^\circ\text{C}, 26^\circ\text{C}, \text{and } 29^\circ\text{C}$. Calculate the mean temperature for the week.

Examine the following questions and identify which one is a statistical question. (a) What is the height of the tallest building in your city? (b) How many hours do students in your class typically sleep at night?

The weights of 5 packages are $2.1$ kg, $1.8$ kg, $3.5$ kg, $2.4$ kg, and $1.5$ kg. Calculate the range of this data.

The number of books read by two students, Priya and Rahul, over 6 months are: Priya: 2, 3, 4, 3, 10, 2 Rahul: 4, 4, 5, 4, 3, 4 Evaluate their reading habits by calculating the mean and median for both. Justify who is the more consistent reader.

The scores of a student in 5 tests are 7, 8, 5, 9, 6. Describe the steps to calculate the mean score.

List two measures of central tendency.

The heights of 7 plants in a garden are 15 cm, 18 cm, 12 cm, 20 cm, 16 cm, 14 cm, 17 cm. Describe the process of finding the median height.

Describe the key differences between the mean and the median as representative values of a dataset. Explain in which situations the median might be a better representative value than the mean.

Two florists, A and B, sold the following number of bouquets over 5 days. Florist A: $12, 15, 10, 18, 20$. Florist B: $16, 14, 13, 15, 17$. Calculate the average number of bouquets sold per day by each florist and determine who performed better on average.

The number of books read by 7 students in a month are: $3, 5, 2, 6, 1, 15, 4$. Calculate the mean and median for this data. Which measure of central tendency do you think better represents the data and why?

The mean score of a cricketer in 5 matches is 42. His scores in the first four matches are 35, 50, 28, and 40. Calculate his score in the fifth match.

A clustered bar graph shows the number of fiction and non-fiction books sold by a bookstore from 2021 to 2023. The data is as follows:

• 2021: Fiction=120, Non-Fiction=100
• 2022: Fiction=150, Non-Fiction=110
• 2023: Fiction=140, Non-Fiction=130

1. Evaluate the trend for fiction book sales and non-fiction book sales separately over the three years.
2. In which year was the difference between fiction and non-fiction sales the greatest?
3. Formulate a prediction for the sales in 2024, justifying your reasoning.
4. Propose one business decision the bookstore owner could make based on this data.

Define a statistical statement and provide two new examples.

Summarize the steps required to create a double bar graph to compare the number of boys and girls in three different sections of Class 7 (Section A, B, C). List the essential components that must be included in the graph.

A basketball player scored the following points in 6 games: $22, 14, 18, 25, 16, 20$. Calculate the median score.

A bar graph shows the number of cars sold by different companies, but the vertical axis starts at 100 instead of 0. Propose a reason why this might be considered a misleading representation.

A double bar graph compares the monthly sales of laptops and tablets for a store over a year. Formulate three distinct conclusions you can draw from such a graph. Justify each conclusion by describing what you would look for in the graph.

What is an outlier in a set of data?

Explain why a double bar graph is used.

Explain how to find the median of a dataset with an even number of values. Provide a simple example.

Summarize the information presented in a dot plot.

A dataset is given as: 5, 7, 8, 6, 100. Identify the outlier and explain how it might affect the mean.

A group of 4 friends collected 20, 25, 15, and 32 shells from a beach. Another group of 5 friends collected 18, 22, 24, 19, and 27 shells. If each group decides to share their shells equally amongst themselves, which group's members will get more shells each? Calculate the share per person for each group.

The heights (in cm) of 8 plants in a garden are: $35, 42, 38, 40, 45, 32, 38, 48$. Calculate the mean and median height of the plants.

The marks obtained by a student in Term 1 and Term 2 examinations (out of 100) are given below.

A student wants to investigate the sleeping habits of their classmates. Formulate one statistical question they could ask to begin their investigation.

Team A's average score in 5 matches is 150 runs. Team B's average score in the same 5 matches is 145 runs. A fan claims Team A is definitively the better team. Critique this conclusion.

Design a dataset of 7 distinct positive integers with the following properties:

• The mean is 15.
• The median is 12.
• The range is 20. Justify that your dataset meets all three conditions.

Two basketball players, Anjali and Brijesh, have the following points per game in a tournament: Anjali: 15, 17, 16, 18, 14 Brijesh: 25, 5, 30, 2, 18 Evaluate their performances. Who would you choose for a team that needs a reliable, consistent scorer? Justify your choice using statistical measures like mean and range.

Create two datasets, each with 7 data points, representing the daily sales (in ₹) of two small shops, Shop A and Shop B, over 7 days. Ensure Shop B's dataset has a significant outlier.

1. Calculate the mean, median, and range for both shops.
2. Evaluate which shop has more consistent sales.
3. Justify which measure (mean or median) is a better representative of daily sales for each shop and explain why.
4. Propose which shop is likely more stable, based on your analysis.

Explain the difference between a value of '0' and 'no value' (or a missing value) in a dataset when calculating the average. Use an example.

Formulate a dataset of 5 distinct positive integers where the mean is exactly 10 and the median is 12.

A dot plot shows the number of pets owned by students in a class. There are 3 dots at 0, 5 dots at 1, 4 dots at 2, 2 dots at 3, and 1 dot at 5. Calculate the mean number of pets per student.

A school principal wants to determine if a new 'extra math class' program is effective. The scores of 8 students in a pre-test (before the program) and a post-test (after the program) are recorded.

1. Formulate a hypothetical but realistic dataset for the pre-test and post-test scores (out of 50).
2. Design a double bar graph to visually compare the scores for each student.
3. Calculate the mean score for both tests.
4. Evaluate the program's effectiveness based on your created data and graph. Propose a concluding statement for the principal.

The scores of a student in 8 tests are: 85, 88, 92, 84, 90, 25, 89, 91. Propose a valid argument for excluding the score of 25 when calculating the student's average performance. Justify your argument by calculating the mean with and without this score and explaining the impact.

The salaries (in thousands of Rupees) of 7 employees in a small company are: $30, 32, 35, 38, 40, 42, 150$. (a) Calculate the mean and median salary. (b) Identify the outlier in the data. (c) Recalculate the mean and median after removing the outlier. (d) Analyze and explain the effect of the outlier on the mean and median.

The following table shows the profit (in thousands of ₹) of a company over four quarters of a year. Q1: 50, Q2: 55, Q3: 48, Q4: 150 (due to a one-time large contract) A manager presents a simple bar graph and claims the company's performance is showing 'incredible, consistent growth', using the mean profit as evidence.

1. Critique the manager's claim.
2. Calculate both the mean and the median profit.
3. Propose a better way to describe the company's typical quarterly performance.
4. Justify why the median or a statement acknowledging the outlier would provide a more accurate picture.

The running times (in minutes) for two athletes, Rohan and Sameer, for six 5km runs are recorded. Rohan: $25, 28, 24, 25, 30, 26$. Sameer: $29, 23, 27, 26, 28, 27$. (a) Calculate the mean running time for both athletes. (b) Calculate the median running time for both athletes. (c) Calculate the range for both to examine consistency. (d) Based on your analysis, compare their performances. Who is faster on average? Who is more consistent?

A student's weekly pocket money for 6 weeks is: ₹50, ₹60, ₹55, ₹50, ₹150, ₹55. Describe the step-by-step process to find both the mean and the median of this data. Identify any outliers and explain their impact.

Create a small dataset showing the number of hours spent on homework by 5 students on a weekday vs. a weekend. Design a clustered bar graph to represent this data. Justify your choice of scale for the vertical axis.