A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is 76.

Question

Quizplus · Accepted Answer

This statement is false.

The formula to calculate the sum of squared deviations (SS) from the sample mean is:

SS = Σ(xᵢ - x̄)²

where Σ denotes the sum of all observations, xᵢ is the value of the i-th observation, and x̄ is the sample mean.

We are given that the sample size is n = 20 and the sample standard deviation is s = 4. However, we do not have information about the sample mean or the actual values of the observations.

The formula to calculate the variance of a sample is:

s² = SS/(n-1)

and the formula to calculate the standard deviation of a sample is:

s = √(SS/(n-1))

Using the information given, we can solve for SS:

s² = SS/(n-1)
4² = SS/(20-1)
16(19) = SS
SS = 304

Therefore, the statement that the sum of squared deviations from the sample mean is 76 is false, since the actual value is 304.

A Sample of 20 Observations Has a Standard Deviation of 4