A sample of 15 observations has a standard deviation of 4.The sum of the squared deviations from the sample mean is:
A) 19
B) 56
C) 60
D) 224
E) 240

Question

Quizplus · Accepted Answer

We know that the formula for calculating the sum of squared deviations from the mean is:
SS = Σ(x - x̄)²
where Σ represents the sum, x is each data value in the sample, and x̄ is the sample mean.

We are given the standard deviation, which we can use to find the variance:
s² = (standard deviation)² = 4² = 16

We also know that the variance is equal to the sum of squared deviations from the mean divided by the sample size minus 1:
s² = SS/(n-1)

Solving for SS, we get:
SS = s² x (n-1) = 16 x (15-1) = 224

Therefore, the sum of squared deviations from the sample mean is 224.

A Sample of 15 Observations Has a Standard Deviation of 4.The