The Basic Practice of Statistics
The Basic Practice of Statistics
8th Edition
ISBN: 9781319057916
Author: Moore
Publisher: MAC HIGHER
Question
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Chapter 2, Problem 2.52E

a.

To determine

To find: The five-number summary for the distribution of revenues for the top global 500

To explain: Why the five-number summary suggests that the distribution is right skewed.

a.

Expert Solution
Check Mark

Answer to Problem 2.52E

The five-number summary for the distribution of revenues for the top global 500 is 139.4 149.1 182.0 286.3 485.7 .

The difference between the median and minimum is less than the difference between maximum and median in the five-number summary suggests that the distribution is right skewed.

Explanation of Solution

Given info: Table 2.3gives the highest revenues for 30 companies from global 500 companies in 2014.

Calculation:

Five-number summary:

The five-number summary of a distribution consists of minimum, the first quartile, the median, the third quartile, and the maximum. The order of five-number summary is as follows:

Minimum Q1M Q3Maximum .

Software procedure:

Step-by-step software procedure for five-number summary using MINITAB software is as follows:

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the columns GLOBE500.
  • Choose option statistics, and select minimum, first quartile, median, third quartile, maximum.
  • Click OK.

Output using MINITAB software is as follows:

The Basic Practice of Statistics, Chapter 2, Problem 2.52E , additional homework tip  1

The five-number summary for the distribution of the highest revenues of 30 companies for the top global 500 is 139.4 149.1 182.0 286.3 485.7 .

Justification:

The distance from median and minimum is,

MedianMinimum=182.0139.4=42.6

The distance from the maximum to the median is,

MaximumMedian=485.7182.0=303.7

From the five-number summary, the distribution is right skewed because the difference between the median and minimum is less than the difference between the median and maximum.

b.

To determine

To find: The companies which are outliers according to the 1.5×IQR rule.

To check: Whether the 1.5×IQR rule suggest the same about the companies that are outliers or not.

b.

Expert Solution
Check Mark

Answer to Problem 2.52E

According to 1.5×IQR rule, there are no companies that are considered as outliers.

Yes, the 1.5×IQR rule’s suggestion is agreed with stemplot.

Explanation of Solution

Calculation:

From the output in part (a) Q1=149.1 and Q3=286.3

Interquartile range (IQR):

The difference between the first quartile and the third quartile is considered as interquartile range.

Thus,

IQR=Q3Q1=286.3149.1=137.2

For revenues of 30 companies, IQR=137.2 .

The 1.5×IQR rule for outliers:

A observation is a suspected as outlier if it is more than Q3+(1.5×IQR) or less than Q1(1.5×IQR) .

Q3+(1.5×IQR)=286.3+(1.5×137.2)=286.3+205.8=492.1

Q1(1.5×IQR)=149.1(1.5×137.2)=149.1205.8=56.7

The 1.5×IQR rule suspects no outliers in the distribution of revenues for the companies. Because there are no values that are out of the limit Q3+(1.5×IQR)=492.1 and Q1(1.5×IQR)=56.7 .

Stemplot:

Software procedure:

Step-by-step software procedure to draw stemplot using MINITAB software is as follows:

  • Select Graph>Stem and leaf.
  • Select the column of GLOBE500 in Graph variables.
  • Select OK.

Output of stemplot is shown below:

The Basic Practice of Statistics, Chapter 2, Problem 2.52E , additional homework tip  2

Justification:

The stemplot does not show any outliers which indicates that the 1.5×IQR rule’s suggestion that there are no outliers is agreed.

c.

To determine

To explain: The common feature that the 30 companies in the Table 2.3 share.

To find: The proportion of the total of the global 500 revenues accounted by the 30 companies.

c.

Expert Solution
Check Mark

Answer to Problem 2.52E

The common feature that the 30 companies share is that they are the high outliers and have high revenues out of global 500 companies.

The proportion of the total global 500 revenues by the 30 companies is 0.06.

Explanation of Solution

Justification:

From the global 500 companies, 30 companies in Table2.3 have high revenues than the remaining companies, and these 30 companies are the high outliers that has a common feature of sharing.

The proportion of the total global 500 companies accounted by the 30 companies is:

Proportion=30500=0.06

Thus, the proportion of the total global 500 revenues by the 30 companies is 0.06.

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