Question

given a mean of 7.6 and a standard deviation of 3.1, within how many standard deviations of the mean do the values 10,9,11,5, and 3 fall? please explain how you got the answer.

Answer 1

if the mean is 7.6 the 1 standard deviation from the mean is

lower bound =7.6 - 3.1 and Upper bound = 7.6 + 3.1

so if a number is between 4.5 and 10.7 it is within 1 standard deviation of the mean.

2 standard deviations

lower bound = 7.6 - 2 x 3.1 = 1.4 Upper bound = 7.6 + 2 x 3.1 13.8

so the boundary for 2 standard deviations are 1.4 to 4.5 then 10.7 to 13.8

so look at each number individually 10... between 4.5 and 10.7 so 1 SD
9 between 4.5 and 10.7 so 1 SD

just keep going.