Question

The following data are costs (in cents) per ounce for nine different brands of sliced Swiss cheese. 27 64 38 44 70 81 47 52 49

a) Calculate the variance for this data set. (Round your answer to three decimal places.)

b) Calculate the standard deviation for this data set. (Round your answer to three decimal places.)

Answer 1

Solution:
Given in the question
Cost per ounce for nine Different brands of sliced swiss chees
27, 64, 38, 44, 70, 81, 47, 52, 49
First we will calculate mean of the data
Mean = Xi/n = (27+64+38+44+70+81+47+52+49)/9 = 472/9 = 52.44
Solution(a)
Variance of data set can be calculated as
Variance = ((Xi-mean)^2)/(n-1)

Variance = ((27-52.44)^2 + (64-52.44)^2 + (38-52.44)^2 + (44-52.44)^2 + (70-52.44)^2+(81-52.44)^2+(47-52.44)^2 + (52-52.44)^2+(49-52.44)^2)/(9-1) = 2226.2224/8 = 278.279

X	Xi-mean	(Xi-mean)^2
27	-25.44	647.1936
64	11.56	133.6336
38	-14.44	208.5136
44	-8.44	71.2336
70	17.56	308.3536
81	28.56	815.6736
47	-5.44	29.5936
52	-0.44	0.1936
49	-3.44	11.8336

Solution(b)
Standard deviation for this data set can be calcualted as
Standard deviation = sqrt(Variance) = 16.682