CBSE Class 10 Maths 2024-25: Chapter 13 Statistics Competency-Based Questions with Answers; Download Free PDF

As the CBSE Class 10 board exams get closer, students need to understand the new exam pattern. Starting in the 2024-25 school year, CBSE will include 50% more competency-based questions. These questions will be both multiple choice and written, focusing on how to use what students have learned in real-life situations.

This article explores Chapter 13 Statistics. It highlights key competency-based questions and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 13 Statistics

Competency-based questions are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as case studies, true-false questions, gap-filling tasks, and long or short answer questions.

Competency-based questions in Chapter 13 Statistics go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 13: Statistics Important Competency-Based Questions

Multiple Choice Questions

Q.1 The table below shows the results of a survey conducted on 40 gamers on how many games did they play on a particular day.

Which of the following is the modal class?

1. 1 - 2
2. 2 - 3
3. 4 - 5
4. 7 - 8

Answer. (2)

Q.2 Shreya collects the following data on the number of movies watched by her friends in the month of June.

What is the average number of movies watched by Shreya's friends in that particular month?

1. 4.16
2. 4.20
3. 5
4. 9

Answer. (3)

Q.3 In statistics, an outlier is a data point that differs significantly from other observations of a data set.

If an outlier is included in the following data set, which measure(s) of central tendency would change?

13, 17, 22, 43, 43, 48, 52, 51

1. only mean
2. only mean and median
3. all - mean, median, mode
4. (cannot be said without knowing the outlier)

Answer. (1)

Q.4 In the given number line, p , q and r represent the measures of central tendency of the data: 3, 4, 6, 5, 6, 10.

Which of these is true for p , q and r ?

1. p - Mean
q - Median
r - Mode
2. p - Median
q - Mean
r - Mode
3. p - Mode
q - Median 
r - Mean
4. (cannot be determined unless specific numbers on the scale is provided)

Answer. (2)

Q.5 The approximate relationship between the mean, mode and median can be expressed using an empirical formula.

Shown below are the measures of central tendency of the marks obtained by Class 8 students in a test.

Mean: 5 marks
Mode: 5.3 marks

Which of the following could be the approximate median of the marks? 1 5.10 marks 2 5.15 marks 3 5.20 marks 4 10.15 marks

Answer. (1)

Q.6 A shoe store owner is planning to stock up for the upcoming month. To make an informed decision, she reviews the sales data of various shoe sizes from the past six months.

Which central tendency measure would help her in determining which shoe size to order the most of?

1. Mean
2. Median
3. Mode
4. Any of the above

Answer. (3)

Q.7 The mean of the first four data points in a dataset is 10, while the mean of the remaining sixteen data points is 20.

What is the mean of the entire dataset?

1. 1.5
2. 12
3. 15
4. 18

Answer. (4)

Q.8 The table given below shows the literacy rate of 70 cities in a country.

What is the literacy rate for maximum number of cities?

1. 70.025
2. 72.5
3. 75
4. 112.5

Answer. (2)

Free Response Questions

Q.9 A cooking oil manufacturing company sells oil in three different bottle sizes. Now, it wants to sell only one size in the market. It has data on how the three sizes perform in the market.

Based on which measure of central tendency should the company fix the size of the oil bottle? Justify your answer.

Answer. Writes that the company should fix the size of the oil bottle based on the mode.

Writes that the mode gives the information about the size that is sold most often.

Q.10 Shown below is the frequency polygon. It represents the performance of all participating countries in a question in an international assessment, TIMSS 2011.

If Finland's performance was 58%, did it perform better or worse than the average performance? Show your work.

Answer. 

Writes that Finland performed better than the average performance.

Q.11 Following is the data on the number of maths question attempted by a student in a week.

10, 15, 25, 10, 25, 15, 25

What is the mode of given data?

Answer.  Concludes that 25 comes the maximum number of times hence it is the mode of the data.

Q.12 Farhan draws less than and more than types of ogives on the same graph paper.

What does he obtain from the x-coordinate of the intersection of both the graphs?

Answer. States that Farhan can obtain the median of the data by intersection of less than and more than ogives.

Case Study

Answer the questions based on the given information.

Cricket is a team sport where two teams of 11 players compete to score runs and dismiss opponents. It is played using a bat and a ball. An inning in cricket is when one team bats while the other team bowls.

The table below shows the number of innings played for various ranges of overs in 50 matches of a tournament.

Q.13 Draw a histogram for the given data.

Answer. Interprets the data and draws correct histogram as given:

Q.14 What is the average number of overs played per inning by the team in the tournament? Show your work.

Answer. (Note: Here, Step Deviation method is used. Give full marks for any other method used and solved correctly.)

Takes class size h as 10 and considers a value for assumed mean ( a ). For example, a

= 25 overs.

Q.15 For which range of overs were the most innings played? Which measure of central tendency will definitely be found within that range?

Answer. States that most innings were played for 30-40 overs.

Writes that 30-40 overs is the modal class and hence, the mode will definitely be found within this range.

👉 Read Also- CBSE Class 10 Half-Yearly/Mid Term 2024-25 : Most Important Questions with Answers; PDF Download (All Subjects)

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