Question

A professor records the time (in minutes) that it takes 16 students to complete an exam. Compute the SS, the variance, and the standard deviation assuming the 16 students constitute a population and assuming the 16 students constitute a sample. (Round your answers for variance and standard deviation to two decimal places.)

23	44	42	29
41	20	25	43
40	52	39	36
50	25	14	33

Answer 1

From the given data :

Sample mean(xbar)=$\sum$Xi/n=556/16=34.75

Now the SS (sum of the squares)=$\sum$(Xi-xbar)^2

So the SS (sum of the squares)=1835

Now the sample Variance = SS/(n-1)=1835/(16-1)=1835/15=122.33

Population variance=SS/n=1835/16=114.69

Sample standard deviation=√sample variance=√122.33=11.06

Population standard deviation=√population variance=10.71