Chapter Exam

Chapter 14: Statistics — Online MCQ Test

Q: What is the formula for calculating the mean of grouped data using the direct method?

Answer: A. Mean = Σf × x / Σf — The direct method formula for grouped data mean is the sum of (frequency × class mark) divided by the sum of frequencies.

Q: In a grouped frequency distribution, the class mark (or mid-value) of the class 10-20 is:

Answer: B. 15 — Class mark is calculated as (Lower limit + Upper limit) / 2 = (10 + 20) / 2 = 15.

Q: A frequency distribution table has class intervals: 0-10, 10-20, 20-30, 30-40 with frequencies 5, 8, 12, 10 respectively. What is the total number of observations?

Answer: C. 35 — Total observations = Σf = 5 + 8 + 12 + 10 = 35.

Q: A frequency table shows: Class 20-30 (f=4), 30-40 (f=6), 40-50 (f=5), 50-60 (f=5). Which class is the modal class?

Answer: B. 30-40 — The modal class is 30-40 because it has the highest frequency of 6.

Q: In a grouped frequency distribution, the sum of all frequencies equals 50, and Σ(f × x) = 1250. If the direct method is used, the mean would be _____, but if the class widths were doubled without changing frequencies, the mean would be _____.

Answer: B. 25, 25 — Mean = Σ(f × x) / Σf = 1250/50 = 25. Doubling class widths changes class marks but if frequencies remain the same and data remains consistent, the weighted mean principle shows it stays 25.

MATHS · CLASS 10th · Telangana State Board

Practice Chapter 14: Statistics with a free chapter-wise online MCQ test for Telangana State Board CLASS 10th MATHS. This chapter covers: The final chapter deals with the analysis of grouped data. Students learn to calculate Mean (using direct. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 14: Statistics — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 10th MATHS — Chapter 14: Statistics, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the formula for calculating the mean of grouped data using the direct method?

A. Mean = Σf × x / Σf ✓
B. Mean = Σf + x / Σf
C. Mean = Σx / n
D. Mean = Σf / Σx

Answer: A. Mean = Σf × x / Σf
The direct method formula for grouped data mean is the sum of (frequency × class mark) divided by the sum of frequencies.

In a grouped frequency distribution, the class mark (or mid-value) of the class 10-20 is:

A. 10
B. 15 ✓
C. 20
D. 30

Answer: B. 15
Class mark is calculated as (Lower limit + Upper limit) / 2 = (10 + 20) / 2 = 15.

A frequency distribution table has class intervals: 0-10, 10-20, 20-30, 30-40 with frequencies 5, 8, 12, 10 respectively. What is the total number of observations?

A. 25
B. 30
C. 35 ✓
D. 40

Answer: C. 35
Total observations = Σf = 5 + 8 + 12 + 10 = 35.

A frequency table shows: Class 20-30 (f=4), 30-40 (f=6), 40-50 (f=5), 50-60 (f=5). Which class is the modal class?

A. 20-30
B. 30-40 ✓
C. 40-50
D. 50-60

Answer: B. 30-40
The modal class is 30-40 because it has the highest frequency of 6.

In a grouped frequency distribution, the sum of all frequencies equals 50, and Σ(f × x) = 1250. If the direct method is used, the mean would be _____, but if the class widths were doubled without changing frequencies, the mean would be _____.

A. 25, 50
B. 25, 25 ✓
C. 1250, 1250
D. 50, 100

Answer: B. 25, 25
Mean = Σ(f × x) / Σf = 1250/50 = 25. Doubling class widths changes class marks but if frequencies remain the same and data remains consistent, the weighted mean principle shows it stays 25.