Thread: standard deviation

If you have a random sample of 1000 social work clients, and the average value of some sample statistic (e.g., age, weight, income, etc.) is ‘50’, with a standard deviation of 10, about how many people from your sample will be included in the range of values between 40 and 60 on this measure of the sample statistic? Why? About how many will be included between the range of 30 – 70? Why?

This question is for very basic understanding of the Standard Deviation. You should not be struggling with this. It is a standard z-score.

Mean = 50
Standard Deviation = 10
Between 40 and 60

Recognize this immediately as one standard deviation on each side of the Mean. There is an Empirical Rule for that, 68-95-99.7 rule - Wikipedia, the free encyclopedia, making it an eyeball problem, but only if you know the rule.

Between 30 and 70

Recognize this immediately as two standard deviations on each side of the Mean. Please consult the Empirical Rule for an instant answer.