For a discrete frequency distribution, the total number of observations is 20 , the mean is 10 , and the variance is 13.5 . Later, it was discovered that the frequency of the observation value 19 was incorrectly recorded as 4 instead of 2 .

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For a discrete frequency distribution, the total number of observations is 20 , the mean is 10 , and the variance is 13.5 . Later, it was discovered that the frequency of the observation value 19 was incorrectly recorded as 4 instead of 2 . The correct variance of the distribution is

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Correct answer: B. 5

Let the initial total number of observations be N = 20 . Initial mean x = 10 and initial variance ^2 = 13.5 . Sum of observations f_i x_i = 20 10 = 200 . Sum of squares of observations f_i x_i^2 = 20 (13.5 + 10^2) = 20 113.5 = 2270 . The frequency of the observation 19 was incorrectly recorded as 4 instead of 2 . This means two extra instances of the value 19 were included. To correct the data, we must remove two instances of 19 . New total number of observations N_ new = 20 - 2 = 18 . New sum of observations = 200

For a discrete frequency distribution, the total number of observations is 20 , the mean is 10 , and the variance is 13.5 . Later, it was discovered that the frequency of the observation value 19 was incorrectly recorded as 4 instead of 2 . The correct variance of the distribution is

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