statistics

Question

A massage therapist charges $100 for one hour session, but as a reward to his customers, every third and fourth session is reduced to a charge of $70 and every fifth session is free. If every customer comes for a very large number of sessions, what is the standard deviation on the price? Round your answer to three decimal places.

Answer 1

Hello, thank you for your question!

In order to compute the standard deviation we first want to find the mean and then the variance.

Mean is a simple average of the 5 values so you can take (100 + 100 + 70 + 70 + 0)/5 = $68

The variance then would come from taking the sum of (xi – mean)^2 for each value in the list and then dividing by the sample size. For this data set that would be

(100 – 68)^2 + (100 – 68)^2 + (70 – 68)^2 + (70 – 68)^2 + (0 – 68)^2 = 6680/5 = 1336

Finally then we can take the square root of the variance to find the standard deviation

sqrt(1336) = 36.55