Question

Suppose that a sample of 10 observations has a standard deviation of 3, then the sum of the squared deviations from the sample mean is 30.
TRUE or FALSE?

Answer 1

Answer:

False

Step-by-step explanation:

Standard deviation (SD) = 3

Sample size (n) = 10

The standard deviation of a sample is determined as the square root of the sum of the squared deviations from the sample mean (S) divided by number of degrees of freedom (n-1). The sum of the squared deviations is:

$SD= \sqrt{\frac{S} {n-1}}\\ 3= \sqrt{\frac{S} {10-1}}\\S=9*9 = 81$

The sum of the squared deviations from the sample mean is 81. Therefore, the statement is false.