Question

Consider the following data:

12,9,7,8,5,112,9,7,8,5,1

Step 1 of 3:

Calculate the value of the sample variance. Round your answer to one decimal place.

Step 2 of 3:

Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Step 3 of 3:

Calculate the value of the range.

Answer 1

For the following data 12,9,7,8,5,112,9,7,8,5,1, to calculate the variance and standard deviation we need to find the mean first as:

Mean = (12 + 9 + 7 + 8 + 5 + 112 + 9 + 7 + 8 + 5 + 1)/11
= 183/11
Mean = 16.6364

Step1:

The sample variance is calculated as;

Sample variance = (1/11 - 1) x ((12 - 16.6364)2 + (9 - 16.6364)2 + (7 - 16.6364)2 + (8 - 16.6364)2 + (5 - 16.6364)2 + (112 - 16.6364)2 + (9 - 16.6364)2 + (7 - 16.6364)2 + (8 - 16.6364)2 + (5 - 16.6364)2 + (1 - 16.6364)2)
= (1/10) x ((-4.6364)2 + (-7.6364)2 + (-9.6364)2 + (-8.6364)2 + (-11.6364)2 + (95.3636)2 + (-7.6364)2 + (-9.6364)2 + (-8.6364)2 + (-11.6364)2 + (-15.6364)2)
= (0.1) x ((21.49620496) + (58.31460496) + (92.86020496) + (74.58740496) + (135.40580496) + (9094.21620496) + (58.31460496) + (92.86020496) + (74.58740496) + (135.40580496) + (244.49700496))
= (0.1) x (10082.54545456)
= 1008.3

Step2:

The sample standard deviation is calculated as:

S = √S2

= √(1008.254545456)
= 31.8

Step-3

Range is calculated as Maximum - Minimum value

Range = 112-1 = 111