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If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and 37/4 respectively, then (a − b)^2 is equal to :
- (1) 24
- (2) 12
- (3) 32
- (4) 16
Correct answer: (4) 16
Solution
The mean of the data set is calculated by averaging all the values, including a and b, which must equal 9. The variance, which measures the spread of the data, is given as 37/4. By solving the equations derived from these conditions, we find that (a - b)^2 equals 16, confirming option D as correct.
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