Chapter Exam

Chapter 13: Statistics — Online MCQ Test

Q: For a class interval 20-30, what is the class mark?

Answer: B. 25 — Class mark = (lower limit + upper limit)/2 = (20 + 30)/2 = 25.

Q: Which formula is used to find the mean of grouped data by the direct method?

Answer: B. Mean = Σfixi/Σfi — For grouped data, the mean is calculated as Σfixi divided by Σfi, where xi is the class mark.

Q: The class with the highest frequency in a grouped frequency distribution is called the:

Answer: B. Modal class — The modal class is the class interval having the maximum frequency.

Q: In the median formula, Median = l + [(n/2 - cf)/f] × h, what does cf represent?

Answer: B. Cumulative frequency before the median class — In the median formula, cf is the cumulative frequency of the class preceding the median class.

Q: Find the mean of the grouped data: class intervals 0-10, 10-20, 20-30 with frequencies 4, 6, 10 respectively.

Answer: B. 18 — Class marks are 5, 15 and 25. Mean = (4×5 + 6×15 + 10×25)/(4+6+10) = 360/20 = 18.

Q: For the distribution 0-10: 5, 10-20: 8, 20-30: 12, 30-40: 5, what is the median?

Answer: B. 21.67 — Here n = 30 and n/2 = 15. Median class is 20-30, so Median = 20 + [(15 - 13)/12] × 10 = 21.67.

Q: If the classes 0-10, 10-20, 20-30, 30-40 have frequencies 5, x, 10, 5 and the mean is 20, find x.

Answer: C. 10 — Using class marks 5, 15, 25, 35, mean = (450 + 15x)/(20 + x) = 20. Solving gives x = 10.

Q: For the distribution 0-10: 5, 10-20: x, 20-30: 20, 30-40: 10, the median is 22. Find x.

Answer: C. 17 — Here n = 35 + x and median class is 20-30. Using 22 = 20 + [((35 + x)/2 - (5 + x))/20] × 10 gives x = 17.

Q: For the distribution 0-10: 4, 10-20: 8, 20-30: x, 30-40: 10, 40-50: 6, the median is 27. Find x.

Answer: B. 10 — Here n = 28 + x and median class is 20-30. Using 27 = 20 + [((28 + x)/2 - 12)/x] × 10 gives x = 10.

Q: For the distribution 0-10: 12, 10-20: 18, 20-30: 18, 30-40: 6, if 10-20 is taken as the modal class for applying the NCERT mode formula, what value is obtained?

Answer: B. 20 — Using l = 10, f1 = 18, f0 = 12, f2 = 18, h = 10, Mode = 10 + [(18 - 12)/(36 - 12 - 18)] × 10 = 20.

MATHS · Grade 10 · CBSE(NCERT)

Practice Chapter 13: Statistics with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 10 MATHS. This chapter covers: Grouped data Frequency distribution Class interval Mean Median Mode Cumulative frequency Ogive Histogram. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 13: Statistics — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 10 MATHS — Chapter 13: Statistics, with answers and explanations. These are sample questions; the exam has its own separate question set.

For a class interval 20-30, what is the class mark?

A. 20
B. 25 ✓
C. 30
D. 10

Answer: B. 25
Class mark = (lower limit + upper limit)/2 = (20 + 30)/2 = 25.

Which formula is used to find the mean of grouped data by the direct method?

A. Mean = Σfi/Σxi
B. Mean = Σfixi/Σfi ✓
C. Mean = Σxi/Σfi
D. Mean = Σfi/Σfixi

Answer: B. Mean = Σfixi/Σfi
For grouped data, the mean is calculated as Σfixi divided by Σfi, where xi is the class mark.

The class with the highest frequency in a grouped frequency distribution is called the:

A. Median class
B. Modal class ✓
C. Mean class
D. Cumulative class

Answer: B. Modal class
The modal class is the class interval having the maximum frequency.

In the median formula, Median = l + [(n/2 - cf)/f] × h, what does cf represent?

A. Frequency of the median class
B. Cumulative frequency before the median class ✓
C. Total frequency
D. Class size

Answer: B. Cumulative frequency before the median class
In the median formula, cf is the cumulative frequency of the class preceding the median class.

Find the mean of the grouped data: class intervals 0-10, 10-20, 20-30 with frequencies 4, 6, 10 respectively.

A. 16
B. 18 ✓
C. 20
D. 22

Answer: B. 18
Class marks are 5, 15 and 25. Mean = (4×5 + 6×15 + 10×25)/(4+6+10) = 360/20 = 18.

For the distribution 0-10: 5, 10-20: 8, 20-30: 12, 30-40: 5, what is the median?

A. 20.67
B. 21.67 ✓
C. 22.67
D. 23.67

Answer: B. 21.67
Here n = 30 and n/2 = 15. Median class is 20-30, so Median = 20 + [(15 - 13)/12] × 10 = 21.67.

If the classes 0-10, 10-20, 20-30, 30-40 have frequencies 5, x, 10, 5 and the mean is 20, find x.

A. 5
B. 8
C. 10 ✓
D. 12

Answer: C. 10
Using class marks 5, 15, 25, 35, mean = (450 + 15x)/(20 + x) = 20. Solving gives x = 10.

For the distribution 0-10: 5, 10-20: x, 20-30: 20, 30-40: 10, the median is 22. Find x.

A. 15
B. 16
C. 17 ✓
D. 18

Answer: C. 17
Here n = 35 + x and median class is 20-30. Using 22 = 20 + [((35 + x)/2 - (5 + x))/20] × 10 gives x = 17.

For the distribution 0-10: 4, 10-20: 8, 20-30: x, 30-40: 10, 40-50: 6, the median is 27. Find x.

A. 8
B. 10 ✓
C. 12
D. 14

Answer: B. 10
Here n = 28 + x and median class is 20-30. Using 27 = 20 + [((28 + x)/2 - 12)/x] × 10 gives x = 10.

For the distribution 0-10: 12, 10-20: 18, 20-30: 18, 30-40: 6, if 10-20 is taken as the modal class for applying the NCERT mode formula, what value is obtained?