Question

The following table shows the number of 30-second radio advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association last year.

108 94 96 95 113 127 93 88 117 96 103 139 127 112 155 155 107 125 94 142 130 119 106 134 104 132 125 125 135 136 111 112 148 124 138 103 113 143 120 118 120 89 97 156 117

Prepare a report on the number of advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association. Be sure to answer the following questions in your report. (c) What scales is used to measure number of advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association? What kind of variable is the number of advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association? (d) What are the limits for outliers? (c) What is your conclusion regarding the measure of location of the data?

Answer 1

(c)

(i)

Scale used to measure number of advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association : Ratio scale

(ii)

Kind of variable that is the number of advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association : Discrete kind of variable

(d) What are the limits for outliers?

Lower limit for outlier = 59.25

Upper limit for outlier = 177.25

Explanation:

Arranging numbers in ascending order, we get:

88,89,93,94,94,95,96,96,97,103,103,104,106,107,108,111,112,112,113,113,117,117,118,119,120,120,124,125,125,125,127,127,130,132,134,135,136,138,139,142,143,148,155,155,156

The bottom half is given by:

88,89,93,94,94,95,96,96,97,103,103,104,106,107,108,111,112,112,113,113,117,117

The middle of these numbers = 103.5

So,

Q1 = 103.5

The upper half is given by:

118,119,120,120,124,125,125,125,127,127,130,132,134,135,136,138,139,142,143,148,155,155,156

The middle of these numbers = 133

So,

Q3 = 133

So,

IQR = Q3 - Q1 = 133 - 103.5 = 29.5

Lower Fence = Q1 - (1.5 X IQR) = 103.5 - (1.5 X 29.5) = 103.5 - 44.25 = 59.25

Upper Fence = Q3 + (1.5 X IQR) = 133 + (1.5 X 29.5) = 133 + 44.25 = 177.25

Lower limit for outlier = 59.25

Upper limit for outlier = 177.25

(c) What is your conclusion regarding the measure of location of the data?

Mean = 5341/45 = 118.6889

Explanation:
Since there is no outlier, Mean is suitable measure of location of the data.