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The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is:
- 3.99
- 3.98
- 4.01
- 4.02
Correct answer: 3.99
Solution
Original sum = 20*10 = 200, sum of squares = 20*(4+100) = 2080. Replacing 9 with 11: new sum = 202, new sum of squares = 2080-81+121 = 2120. New mean = 10.1, variance = 2120/20 - 10.1^2 = 106 - 102.01 = 3.99.
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