Question

The following data give the times (in minutes) that all 10 students took to complete an assignment in a statistics class.

15 25 16 36 32 13 29 19 21 39

Carry out all calculations exactly, round to 2 decimal places the final answers where it is necessary.

a. Calculate the range, variance, and standard deviation for these data.

Variance is not: 84.06

Answer 1

a) The range of data is computed as:
Range = Max - Min = 39 - 13 = 26

Therefore 26 is the required range here.

The computations would be made using the following table here:

X	(X - Mean(X))^2
15	90.25
25	0.25
16	72.25
36	132.25
32	56.25
13	132.25
29	20.25
19	30.25
21	12.25
39	210.25
245	756.5

The sample mean is computed as: (Using the first column sum )

The sample variance now is computed here as: ( from the second column sum)

Therefore  84.06 is the required variance here.

The standard deviation now is computed here as:

Therefore 9.1682 is the required standard deviation here.