The market capitalizations of 20 companies, in billions of dollars, are listed t
ID: 3297193 • Letter: T
Question
The market capitalizations of 20 companies, in billions of dollars, are listed to the right. Complete parts (a) and (b).
264.6
92.6
288.2
136.7
233.3
75.4
112.4
127.9
217.6
108.2
61.3
145.1
186.9
106.9
3.4
10.8
401.3
302.1
2.1
519.1
a. Calculate the mean and standard deviation of the market capitalization for this population of 20 companies.
The mean is ? .
(Round to three decimal places as needed.)
The standard deviation is ?
(Round to three decimal places as needed.)
b. Interpret the parameters calculated in (a). Choose the correct answer below.
A. The standard deviation is large as a portion of the mean. This indicates that the values are relatively spread out.spread out.
B. The standard deviation is small as a portion of the mean. This indicates that the values are relatively spread out.spread out.
C. The standard deviation is large as a portion of the mean. This indicates that the values are relatively concentrated.concentrated.
D. The standard deviation is small as a portion of the mean. This indicates that the values are relatively concentrated.concentrated.
The market capitalizations of 20 companies, in billions of dollars, are listed to the right. Complete parts (a) and (b).
264.6
92.6
288.2
136.7
233.3
75.4
112.4
127.9
217.6
108.2
61.3
145.1
186.9
106.9
3.4
10.8
401.3
302.1
2.1
519.1
Explanation / Answer
a.
The mean is given as,
mean = (264.6 + 92.6 +288.2 +136.7 +233.3 + 75.4 +112.4 +127.9 +217.6 + 108.2 +61.3 +145.1 +186.9 +106.9 + 3.4 + 10.8 + 401.3 +302.1 + 2.1 +519.1) / 20
= 169.795
Standard deviation is given as,
Variance = ((264.6-169.795)^2 + (92.6-169.795)^2 +(288.2-169.795)^2 +(136.7-169.795)^2 +(233.3-169.795)^2 + (75.4-169.795)^2 +(112.4-169.795)^2 +(127.9-169.795)^2 +(217.6-169.795)^2 + (108.2-169.795)^2 +(61.3-169.795)^2 +(145.1-169.795)^2 +(186.9-169.795)^2 +(106.9-169.795)^2 + (3.4-169.795)^2 + (10.8-169.795)^2 + (401.3-169.795)^2 +(302.1-169.795)^2 + (2.1-169.795)^2 +(519.1-169.795)^2) / 19
= 18156.05
SD = sqrt(18156.05) = 134.744
Mean is 169.795
Standard deviation is 134.744
The correct answer is A. The standard deviation is large as a portion of the mean. This indicates that the values are relatively spread out.spread out.
Usually, for a normal spread, standard deviation is one-third of mean. Here, Standard deviation is almost comparable with the mean. So, Standard deviation is large as compared with one-third of the mean (56.598). So the correct option is A.
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