CBSE BOARD PYQS · CHAPTER 13

Statistics
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Statistics. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

The empirical relationship between the three measures of central tendency is:

Q2CBSE 2023, 2019MCQ

1 Mark

Mode of a grouped frequency distribution is given by:

Q3CBSE 2022, 2018MCQ

1 Mark

Class mark of class interval 10 - 25 is:

Q4CBSE 2024, 2021MCQ

1 Mark

If mean of observations x, x+3, x+5, x+7, x+10 is 9, then mean of last 3 observations is:

Q5CBSE 2023, 2017Assertion-Reason

1 Mark

Assertion (A): Mode of a frequency distribution can be determined graphically using a Histogram. Reason (R): The peak rectangle in a histogram corresponds to the modal class.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

Assertion (A): Mean of grouped data can be calculated using Direct Method, Assumed Mean Method or Step Deviation Method. Reason (R): All three methods give the exact same value of mean.

Q7CBSE 2024, 2020Short Answer

2 Marks

Find the mean of first 10 natural numbers.

Q8CBSE 2023, 2019Short Answer

2 Marks

If mean = 27 and median = 33, find mode using empirical formula.

Q9CBSE 2022, 2018Short Answer

2 Marks

Find class mark and class size for class interval 35 - 50.

Q10CBSE 2024, 2021Short Answer

2 Marks

Mean of 100 observations was 50. Later it was found one observation 40 was misread as 50. Find correct mean.

Q11CBSE 2023, 2017Short Answer

2 Marks

Find median class for distribution with total frequency 50 and N/2 = 25.

Q12CBSE 2020, 2016Long Answer

3 Marks

Find mean of distribution: Marks (0-10: 5, 10-20: 10, 20-30: 15, 30-40: 10, 40-50: 10).

Q13CBSE 2024, 2020Long Answer

3 Marks

Find median of distribution: Class (0-10: 4, 10-20: 12, 20-30: 20, 30-40: 10, 40-50: 4).

Q14CBSE 2023, 2019Long Answer

3 Marks

Find mode of distribution: Class (0-20: 6, 20-40: 8, 40-60: 10, 60-80: 12, 80-100: 6, 100-120: 3).

Q15CBSE 2022, 2018Long Answer

3 Marks

If mean of distribution is 50 and sum of frequencies is 120, find missing frequencies f₁ and f₂ for classes (0-20:17, 20-40:f₁, 40-60:32, 60-80:f₂, 80-100:19).

Q16CBSE 2024, 2021Case Study

4 Marks

Case Study Scenario: A literacy survey of 35 cities gave data: Literacy rate % (45-55: 3, 55-65: 10, 65-75: 11, 75-85: 8, 85-95: 3). Question: Find mean literacy rate.

Q17CBSE 2023, 2017Case Study

4 Marks

Case Study Scenario: Life of 400 neon lamps data: Hours (1500-2000: 14, 2000-2500: 56, 2500-3000: 60, 3000-3500: 86, 3500-4000: 74, 4000-4500: 62, 4500-5000: 48). Question: Find median life time of a lamp.

Q18CBSE Official Board PYQPYQ

5 Marks

Median of following data is 525. Find x and y if total frequency is 100: (0-100:2, 100-200:5, 200-300:x, 300-400:12, 400-500:17, 500-600:20, 600-700:y, 700-800:9, 800-900:7, 900-1000:4).

Q19CBSE Official Board PYQPYQ

5 Marks

Mean of following distribution is 18. Find missing frequency f: (11-13:7, 13-15:6, 15-17:9, 17-19:13, 19-21:f, 21-23:5, 23-25:4).

Q20CBSE Official Board PYQPYQ

5 Marks

Statistics CBSE Most Repeated PYQs

The empirical relationship between the three measures of central tendency is:

Mode of a grouped frequency distribution is given by:

Class mark of class interval 10 - 25 is:

If mean of observations x, x+3, x+5, x+7, x+10 is 9, then mean of last 3 observations is:

Assertion (A): Mode of a frequency distribution can be determined graphically using a Histogram. Reason (R): The peak rectangle in a histogram corresponds to the modal class.

Assertion (A): Mean of grouped data can be calculated using Direct Method, Assumed Mean Method or Step Deviation Method. Reason (R): All three methods give the exact same value of mean.

Find the mean of first 10 natural numbers.

If mean = 27 and median = 33, find mode using empirical formula.

Find class mark and class size for class interval 35 - 50.

Mean of 100 observations was 50. Later it was found one observation 40 was misread as 50. Find correct mean.

Find median class for distribution with total frequency 50 and N/2 = 25.

Find mean of distribution: Marks (0-10: 5, 10-20: 10, 20-30: 15, 30-40: 10, 40-50: 10).

Find median of distribution: Class (0-10: 4, 10-20: 12, 20-30: 20, 30-40: 10, 40-50: 4).

Find mode of distribution: Class (0-20: 6, 20-40: 8, 40-60: 10, 60-80: 12, 80-100: 6, 100-120: 3).

If mean of distribution is 50 and sum of frequencies is 120, find missing frequencies f₁ and f₂ for classes (0-20:17, 20-40:f₁, 40-60:32, 60-80:f₂, 80-100:19).

Case Study Scenario: A literacy survey of 35 cities gave data: Literacy rate % (45-55: 3, 55-65: 10, 65-75: 11, 75-85: 8, 85-95: 3). Question: Find mean literacy rate.

Case Study Scenario: Life of 400 neon lamps data: Hours (1500-2000: 14, 2000-2500: 56, 2500-3000: 60, 3000-3500: 86, 3500-4000: 74, 4000-4500: 62, 4500-5000: 48). Question: Find median life time of a lamp.

Median of following data is 525. Find x and y if total frequency is 100: (0-100:2, 100-200:5, 200-300:x, 300-400:12, 400-500:17, 500-600:20, 600-700:y, 700-800:9, 800-900:7, 900-1000:4).

Mean of following distribution is 18. Find missing frequency f: (11-13:7, 13-15:6, 15-17:9, 17-19:13, 19-21:f, 21-23:5, 23-25:4).

The distribution gives daily income of 50 workers: (100-120:12, 120-140:14, 140-160:8, 160-180:6, 180-200:10). Find mean, median and mode.

Statistics
CBSE Most Repeated PYQs