pelican solution

8/12/2019 Pelican Solution

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Solutions to

Case Problems

Chapter 2

Descriptive Statistics: Tabular and Graphical Presentations

Case Problem 1: Pelican Stores

1. There were 70 Promotional customers and 30 Regular customers. Because there are 100observations in the sample, the freuenc! and percent freuenc! distribution are the same. Percent

freuenc! distributions for man! of the variables are given.

"o. of #tems Percent$reuenc!

1 %&% %73 10' 10( &) 7

7 or more *Total+ 100

"et ales Percent$reuenc!

0.00 - %'.&& &%(.00 - '&.&& 30(0.00 - 7'.&& %(7(.00 - &&.&& 10

100.00 - 1%'.&& 1%1%(.00 - 1'&.&& '1(0.00 - 17'.&& 317(.00 - 1&&.&& 3

%00 or more 'Total+ 100

ethod of Pa!ment Percent

$reuenc!/merican press %2iscover 'asterard 1'Proprietar! ard 704isa 10

Total+ 100

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hapter % 2escriptive tatistics+ Tabular and 5raphical Presentations

5ender Percent$reuenc!

$emale &3ale 7

Total+ 100

artial tatus Percent$reuenc!

arried *'ingle 1)

Total+ 100

/ge Percent$reuenc!

%0 - %& 1030 - 3& 30'0 - '& 33(0 - (& 1))0 - )& 770 - 7& '

Total+ 100

These percent freuenc! distributions provide a profile of Pelican6s customers. an! observationsare possible, including+

/ large maorit! of the customers use "ational lothing8s proprietar! credit card.

9ver half of the customers purchase 1 or % items, but a few ma:e numerous purchases.

The percent freuenc! distribution of net sales shows that )1; of the customers spent


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"et ales

ustomer0-%(

%(-(0

(0-7(

7(-100

100-1%(

1%(-17(

17(-%00

%00-%%(

%%(-%(0

%(0-%7(

%7(-300

Total

Promotional 7 17 17 * & 3 % 3 1 % 1 70Regular % 13 * % 3 1 1 30

Total & 30 %( 10 1% ' 3 3 1 % 1 100

$rom the crosstabulation it appears that net sales are larger for promotional customers.'. / scatter diagram of net ales vs. age is shown below. / trendline has been fitted to the data. $rom

this, it appears that there is no relationship between net sales and age.

/ge is not a factor in determining net sales.

Case Problem 2: The Motion Picture Industry

This case provides the student with the opportunit! to use tabular and graphical presentations to anal!=edata from the motion picture industr!. 2eveloping and interpreting freuenc! distributions, percentfreuenc! distributions and scatter diagrams are emphasi=ed. The interpretations and insights can be uitevaried. >e illustrate some below.

Frequency Distribution and Percent Frequency Distribution

The choice of the classes for freuenc! distributions or percent freuenc! distributions can be epected tovar!. The freuenc! distributions we developed are as follows+

Opening Gross Sales

(Millions)

Frequency

(or Percentage)


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'0 ? '&.&& 1(0 ? (&.&& 1)0 ? )&.&& 070 ? 7&.&& 1*0 ? *&.&& 0&0 ? &&.&& 0

100 ? 10&.&& %Total 100

Total Gross Sales

(Millions)

Frequency

(or Percentage)


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&istograms

The following histograms are based on the freuenc! distributions shown above.

0

10

%0

30

'0

(0

)0

70

*0

0-&.&&

10-1&.&&

%0-%0.&&

30-3&.&&

'0-'&.&&

(0-(&.&&

)0-)&.&&

70-7&.&&

*0-*&.&&

&0-&&.&&

100

-10&

.&&

Opening "ee#end Gross Sales (millions)

F

requency

0

10

%0

30

'0

(0

)0

70

*0

&0

0?'&

.&&

(0?&&

.&&

100?1

'&.&&

1(0?1&&

.&&

%00-%'

&.&&

%(0?%&&

.&&

300?3

'&.&&

3(0?3&&

.&&

Total Gross Sales (millions)

Frequency

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0

10

%0

30

'0

(0

)0

0-'&&

(00

-&&&

1000-1'

&&

1(00-1&

&&

%000-%'

&&

%(00

-%&&

&

3000-3'

&&

3(00-3&

&&

Number o T!eaters

Frequency

0

(

10

1(

%0

%(

30

3(

0-' (?& 10?1' 1(?1& %0?%' %(?%&

Number o "ee#s in t!e Top $%

Frequency

'nterpretation

Opening "ee#end Gross Sales The distribution is s:ewed to the right. "umerous motion pictures havesomewhat low opening wee:end gross sales, while a relativel! few @7;A have an opening wee:end grosssales of


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Number o T!eaters This distribution is s:ewed to the right, but not so much as sales data distributions.The number of theaters range from less than (00 to almost '000. (1; of the motion pictures had thesmaller mar:et eposure with the number of theaters less than (00. #nterestingl! enough, %%; of themotion pictures had the widest mar:et eposure, appearing in over 3000 theaters. 3000 to '000 theaters ist!pical for a highl! promoted motion picture.

Number o "ee#s in Top $% This distribution is s:ewed to the right, but not as much as the otherdistributions. #n appears that almost all newl! released movies initiall! ma:e it into the top )0, with )7;sta!ing in the top )0 for ( or more wee:s. ven motion pictures with relative low gross sales can appear inthe top )0 motion pictures for a month or more. /lmost '0; of the motion pictures are in the top )0 for 10or more wee:s, with ); of the motion pictures in the top )0 for %0 or more wee:s.

General Obserations. The data show that there are relative few high-end, highl! successful motionpictures. The financial rewards are there for the pictures that ma:e the bloc:buster level. But the maorit!of motion pictures will have low opening wee:end gross sales and low total gross sales. otion picturesbeing shown in less than 1(00 theaters and motion pictures less than 10 wee:s in the top )0 are common.

Scatter Diagrams

Three scatter diagrams are suggested to show how Total 5ross ales is related to each of the other three

variables.

0.00

(0.00

100.00

1(0.00

%00.00

%(0.00

300.00

3(0.00

'00.00

0.00 %0.00 '0.00 )0.00 *0.00 100.00 1%0.00

Opening "ee#end Gross Sales

TotalGrossSale

0.00

(0.00

100.00

1(0.00

%00.00

%(0.00

300.00

3(0.00

'00.00

0 (00 1,000 1,(00 %,000 %,(00 3,000 3,(00 ',000 ',(00

Number o T!eaters

Tota

lGrossSale

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0.00

(0.00

100.00

1(0.00%00.00

%(0.00

300.00

3(0.00

'00.00

0 ( 10 1( %0 %( 30

Number o "ee#s in t!e Top $%

TotalGrossSal

'nterpretation

Opening "ee#end Gross Sales The scatter plot of total gross sales and opening wee:end gross sales

shows a strong positive relationship. otion pictures with the highest total gross sales were the motionpictures with the highest opening wee:end gross sales. Cow the motion picture does during its openingwee:end should be a ver! good predictor of how the motion picture will do in terms of total gross sales."ote in the scatter diagram that the maorit! of the motion pictures show a low opening wee:end grosssales and a low total gross sales.

Number o T!eaters The scatter plot of the total gross sales and number of theaters also shows a positiverelationship. $or motion pictures pla!ing in less than 3000 theaters, the total gross sales has a positiverelationship with the number of theaters. #f the motion picture is shown in more theaters, higher total grosssales are anticipated. $or motion pictures pla!ing in more than 3000 theaters, the relationship is not asstrong. 3000 to '000 represents the maimum number of theaters possible. #f a motion picture is shown inthis man! theaters, 1( motion pictures did slightl! better in terms of total gross sales. Cowever, thebloc:buster motion pictures in this categor! showed etremel! high total gross sales for the number oftheaters where the motion picture was shown.

Number o "ee#s in Top $% The scatter plot of the total gross sales and number of wee:s in the top )0shows a positive relationship, but this relationship appears to be the wea:est of the three relationshipsstudied. 5enerall!, the more successful, higher gross sales motion pictures are in the top )0 for morewee:s. Cowever, this is not alwa!s the case. $our of the si motion pictures with the highest total grosssales appeared in the top )0 less than %0 wee:s. /t the same time, four motion pictures with %0 or morewee:s in the top )0 did not have unusuall! high total gross sales. This suggests that in some casesbloc:buster movies with high gross sales ma! run their course uic:l! and not have an ecessivel! long runon the top )0 motion picture list. /t the same time, perhaps ualit! motion pictures with a limited audiencema! not generate the high total gross sales but ma! still show a run of %0 or more wee:s on the top )0motion picture list. The number of wee:s in the top )0 does not appear to the best predictor of total grosssales.

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