A researcher computes the definitional formula for SS,as finds that ∑(x-M)= 44.If this is a sample of 12 scores,then what would the value of sample variance be using the computational formula?
A)3.7
B)4.0
C)44
D)not possible to know because the scores are not given

Question

Quizplus · Accepted Answer

The computational formula for sample variance is s^2 = ∑(x-M)^2/(n-1), where s^2 is the sample variance, x is each individual score, M is the mean of the sample, and n is the sample size. We are given that ∑(x-M) = 44, but we are not given the individual scores, so we cannot use the definitional formula to find the mean. However, we can still use the given value to find the sample variance. Since n = 12, we can plug in the values we know:

s^2 = ∑(x-M)^2/(n-1)
s^2 = 44^2/(12-1)
s^2 = 1936/11
s^2 ≈ 176.0/11
s^2 ≈ 16.0
Therefore, the value of the sample variance using the computational formula is approximately 16.0, which corresponds to answer choice B.

A Researcher Computes the Definitional Formula for SS,as Finds That