Chapter 14: Statistics — Online MCQ Test
MATHS · CLASS 10th · Telangana State Board
Practice Chapter 14: Statistics with a free chapter-wise online MCQ test.
This chapter covers: The final chapter deals with the analysis of grouped data. Students learn to calculate Mean (using direct.
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Chapter 14: Statistics — Important Questions & Answers
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.
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.
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.
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.
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.
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.