2012 · Q4
Three sets of data on comparable situations are available as under : Set No. 1 — No. of data 9, Mean Value 8, Standard Deviation 1.6; Set No. 2 — No. of data 12, Mean Value 7, Standard Deviation 1.2; Set No. 3 — No. of data 15, Mean Value 9, Standard Deviation 1.4. Considering all the data sets together, the overall mean value would be :
General Mental Ability, Quantitative Aptitude and StatisticsElementary statistics
- A7.24
- B7.66
- C8.08
- D8.50
Explanation
The overall mean is the weighted average of the group means: (9 × 8 + 12 × 7 + 15 × 9)/(9 + 12 + 15). The numerator is 72 + 84 + 135 = 291 and the denominator is 36, giving 291/36 = 8.0833…, i.e. 8.08. A simple average of 8, 7 and 9 ignores the unequal group sizes and gives the wrong answer. Hence the combined mean is 8.08.