nikhilgmat31 wrote:For the set {2, 2, 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most
increase the standard deviation?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
For any set SYMMETRICAL about the median, mean = median.
Since the values in red are symmetrical about the median of 3.5, the mean of the values in red = the median of the values in red = 3.5.
To increase the SD -- to increase how much the data points DEVIATE from the mean -- the value of x must be AS FAR AS POSSIBLE from the mean of 3.5.
Of the 5 answer choices,
A is farthest from 3.5.
The correct answer is
A.
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