# Divorce Statistics Second Marriages sooo confused…. how can there be 49.5 variance if theres only 35 women??!

as a tiny part of research on marriage, a study looks at marital satisfaction scores on a 1-20 Likert scale for 35 women who were previously divorced and are now married for a second time. Based on the sample of 35 scores, the variance of the larger population of women is estimated to equal 49.5. What is the estimate of the variance of sample means of 35 women’s’ satisfaction scores, should many samples of 35 be taken?

A 49.5
B 35
C 1.41

There’s no problem with the variance being 49.5. That would mean a standard deviation of about 7. That isn’t too far-fetched if the scale is from 1 to 20. So some women put down 12, others 15, maybe 18, maybe 4. There is a lot of variation in their responses.

As to the answer to the multiple-choice question though, it should be 49.5 / 35 = 1.41.
C

(You see because the standard deviation of the sampling distribution is population stdev / sqrt(n), so the VARIANCE of the sampling distribution would be the square of that, which would be:
population variance / n)