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Two groups of 25 students each have mean marks 30 and 40 and variances 16 and 9. Find the variance of all 50 students together.

Competition practiceStatistics

A25
B6.12
C37.5
D12.5

Step-by-Step Solution

Combined mean

= 35

. Variance

= \frac{25 ( 16 + 5 ^{2} ) + 25 ( 9 + 5 ^{2} )}{50} = \frac{41 + 34}{2} = 37.5

. (12.5 just averages 16 and 9, ignoring that the means differ.)

Answer: C) 37.5

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