The mean and standard deviation of five observations are 9 and 0 respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, what is their standard deviation?
2026-03-26 01:11:35.1774487495
The mean and standard deviation of five observations are 9 and 0 respectively.Check body
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Outline:
First, $n = 5, \bar X = 9$ and $S = 0$ imply that the five observations are $9, 9, 9, 9, 9.$
Second, if the new $\bar X = 10,$ then $n\bar X = \sum_{i=1}^5 X_i = 50.$ So, what must the changed observation be? $\sum_{i=1}^5 X_i = 9 + 9 + 9 + 9 + X_5 = 50.$ Solve for $X_5.$
Finally, find the standard deviation of $9,9,9,9,X_5.$