The variance of the data 1001, 1003, 1006, 10 | vedclass

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(A) The variance of a data set remains unchanged if a constant is subtracted from each observation. Let the data be $x_i = 1001, 1003, 1006, 1007, 100

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$10$

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(A) The variance of a data set remains unchanged if a constant is subtracted from each observation. Let the data be $x_i = 1001, 1003, 1006, 1007, 1009, 1010$. Subtracting $1000$ from each observation,we get the new data: $y_i = 1, 3, 6, 7, 9, 10$. The mean of the new data is $\bar{y} = \frac{1+3+6+7+9+10}{6} = \frac{36}{6} = 6$. The variance is given by $\sigma^2 = \frac{\sum y_i^2}{n} - (\bar{y})^2$. $\sum y_i^2 = 1^2 + 3^2 + 6^2 + 7^2 + 9^2 + 10^2 = 1 + 9 + 36 + 49 + 81 + 100 = 276$. $\sigma^2 = \frac{276}{6} - (6)^2 = 46 - 36 = 10$.

The variance of the data $1001, 1003, 1006, 1007, 1009, 1010$ is:

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