CA Foundation P3 · Chapter 14 · Question 10 of 10
Group I has 40 items with mean 50 and SD 6. Group II has 60 items with mean 60 and SD 8. The combined standard deviation is (to two decimals):
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: B) 8.76
Explanation
Combined mean = (40 x 50 + 60 x 60)/100 = 5,600/100 = 56. d₁ = 50 − 56 = −6, d₂ = 60 − 56 = 4. Combined variance = [40(36 + 36) + 60(64 + 16)]/100 = (2,880 + 4,800)/100 = 76.8. Combined SD = √76.8 = 8.76. Ignoring the d² terms gives √52.8 = 7.27, and the weighted average of SDs is 7.20.
More Measures of Central Tendency and Dispersion MCQs
- Q2The median of 23, 11, 37, 19, 42, 28 is:
- Q3In a moderately skewed distribution, the mean is 42 and the median is 40. Using the empirical relationship, the mode is approximately:
- Q4For the distribution below, the median is (to two decimals): Class: 0–10, 10–20, 20–30, 30–40, 40–50 Frequency: 5, 8, 12, 10, 5
- Q5For the distribution below, the mode is (to two decimals): Class: 0–10, 10–20, 20–30, 30–40, 40–50 Frequency: 5, 8, 12, 10, 5
- Q6The largest and smallest values of a data set are 80 and 20. The coefficient of range is: