# ch2 frequency distributions and graphs & ch3 data

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1. Type in all the blood types in column C1 of the worksheet. A B B AB O O O B AB B B B O A O A O O O AB AB A O B A

a) Make a Categorical Frequency Table b) Construct a Pareto chart c) Construct a pie graph.

CChh22 FFrreeqquueennccyy DDiissttrriibbuuttiioonnss aanndd GGrraapphhss && CChh33 DDaattaa DDeessccrriippttiioonn

***Enter the given data into C1 and name the column Blood Type.

a) Making a Categorical Frequency Table

Step 1. Select Stat>Tables>Tally Individual Values

Step 2. Double-click C1 in the Variables list

Step 3. Check the boxes for the statistics: Counts, Percents, and Cumulative percents.

Step 4. Click OK

session window.

2

b) Construct a Pareto chart Step 1. Click on Stat > Quality Tools > Pareto Chart

Step 2. Click the option to Chart defects data in, and double click “C1 Blood Type”

Step 3. Click OK

The pareto chart is displayed in the graph window.

Note: The cumulative percent chart will disappear by doing the following: Step 1. Click on Stat > Quality Tools > Pareto Chart >Options… Step 2. Click “Do not chart cumulative percent” option

Step 3. Click OK

C ou

8 7 4 4 Percent 34.8 30.4 17.4

ABABO

25

20

15

10

5

0

100

80

60

40

20

0

o un

8 7 4 4 Percent 34.8 30.4 17.4

ABABO

9

8

7

6

5

4

3

2

1

0

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

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C) Construct a Pie chart Step 1. Click on Graph>Pie Chart.

Step 2. Click on the inside of the Categorical Variables box, double click “C1 Blood Type”

Step3. Click on Labels> Slice Labels Choose Category name and Percent Check “Draw a line from label to slice”

Click OK.

34.8% O

30.4% B

17.4% AB

17.4% A

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

4

a) Open the worksheet file containing the data from Example 2-2, the high temperature for the 50 states (page 39).

Step1. Click File> Open Worksheet

Step 2. Choose the minitab_portable-datasets folder.

Step 3. Select “E c02-S02-02”

Note: Be sure to choose Minitab Portable[*.mtp] as the Files of type.

Step 4. Click Open.

The data (high temperature for 50 states) is copied in a new

worksheet.

b) Construct a Histogram which displays 7 classes with the class

2. Graph for Quantitative Data a) Open the worksheet file containing the data from Example 2-2, the high temperature for the 50 states (page 39). b) Construct a histogram which displays 7 classes with the class width 5. Use 99.5 as the first lower class boundary. c) Construct a frequency polygon. d) Construct an ogive.

E c02- S02- 02 Example Chapter 2 Section 2 Example 2

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

5

width 5. Use 99.5 as the first lower class boundary.

Step 1.Select Graph>Histogram>Simple

Step 2. Click on Graph variables and double click “C1 TEMERATURES”

Step 3. Click Scale… Select the Gridlines tab. Check Y major ticks and X major ticks.

Select the Y-Scale Type tab. Check Frequency

Click OK.

Step 4. Click Labels. Type the title -Record High Temperature

Type Your name and Date in the footnotes Click OK.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

6

Step 5. Click on Data Options. Click the tab for Group Options. Uncheck both options.

Click OK.

window.

The Edit Scale dialgoue is displayed.

Step 8. Click the tab for Binning, then the option for Cutpoint.

Click the button for Midpoint/Cutpoint positions.

Type in the textbox: 99.5:134.5/5. This is the shortcut for entering the sequence of 99.5 to 134. 5 by 5. These are boundaries for each class.

Step 9. Click OK.

graph window.

7

Class boundaries X(Class Midpoint) Frequency 99.5–104.5 10 2 104.5–109.5 107 8 109.5–114.5 112 18 114.5–119.5 117 13 119.5–124.5 122 7 124.5–129.5 127 1 129.5–134.5 132 1

c) Construct a Frequency Polygon Step 1. Select File>New>Minitab Worksheet.

Step 2. Enter the midpoints of each class in C1 and the corresponding frequencies in C2. Use one midpoint higher (i.e. 137) and lower (i.e. 97). They will be needed to anchor the endpoints.

Step 3. Select Graph>Scatterplot>With Connect line.

Step 4. Double click “C1 f” for Y variables and “C1 X” for X-variables.

Step 5. Click Data View, then the Data Display tab. Check two options: Symbols and Connect line. Click OK.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

8

Step 6. Click Scale. Click the tab for Gridlines then check the major ticks for X and Y.

Click the tab for Reference Lines then type 0 for the Y positions.

Click OK twice.

window.

The Edit Scale dialgoue is displayed.

In the Scale tab, click the option for Positions of ticks. Type 97:137/5

Click OK.

X

f

140130120110100

20

15

10

5

0

9

The ogive (cumulative frequency graph) can be constructed by

following the steps for a frequency polygon with two minor changes:

Step 1. Make the following changes in the worksheet.

Change the X values to the class limits from 99.5 to 134.5 by 5. Change the frequencies to cumulative frequencies.

Step 2. Select Graph>Scatterplot>With Connect line.

Step 3. Click Labels. Change the title. – Ogive of Record High Temperatures.

Step 4. Click OK.

Step 5. Double click on the x-scale.

The Edit Scale dialgoue is displayed.

In the Scale tab, click the option for Positions of ticks. Type 99.5:134.5/5

Click OK.

X

f

134.5129.5124.5119.5114.5109.5104.599.5

50

40

30

20

10

Your Name Date

Your Name Date

10

***Enter the given data and name the column Sit Ups.

a) Construct a stem and leaf plot. Step 1. Click on Graph>Stem-and-Leaf.

Step 2. Click on the inside of the Graph variables and double click “C1 Sit Ups”

You have the option of checking Trim outliers if the exercise requires you to do so.

Step 3. Click in the Increment text box, and enter 10 (the class width).

Step 4. Click OK.

The stem and leaf plot is displayed in the session

window

3. The maximum numbers of sit-ups completed by the participants in an exercise class after 1 month in the program are recorded:

24 31 54 62 36 28 37 55 18 27 58 32 37 41 55 39 56 42 29 35

a) Construct a stem and leaf plot. b) Calculate the sample mean and sample standard deviation. c) Find the five-number summary. d) Construct a boxplot e) Identify any outlier(s) obtained from the boxplot. f) Use the Interquartile range to determine whether 62 is an outlier or not. Explain.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

11

Step 1. Click on Stat>Basic Statistics>Display Descriptive Statistics.

Step 2. Click on the Variable box and double click “C1 Sit Ups”

Step 3. Click Statistics and check option boxes for Mean, Standard deviation, Variance, First quartile, Median, Third quartile, Interquartile range, Minimum, Maximum, and N nonmissing.

*Uncheck other options. Click OK

Step 4. Click OK.

The results are displayed in the session window.

The sample mean value is 39.80. The sample standard deviation is 12.76.

c) Find the five-number summary.

Follow the same procedures in part b) and obtain the

five-number summary.

Minimum Q1 Median Q3 Maximum 18.00 29.50 37.00 54.75 62.00

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

12Sit Ups 6050403020

Boxplot of Sit Ups

d) Construct a boxplot Step1. Click on Graph>Boxplot Click OK to select simple box plot.

Step 2. Click on Graph Variables and double click “C1 Sit Ups”

Step 3. Click on Data View and check Interquartile range box and Outlier symbols in the data display

menu.

The boxplot is displayed in the graph window.

Note: The boxplot can be transposed horizontally. Step 1. Double click the horizontal edge of the box frame

Step 2. Check “Transpose value and category scales in the Edit Scale.

Step 3. Click OK.

13

e) Identify any outlier(s) obtained from the boxplot. Values beyond the whiskers are outliers and it is indicated by the asterisk symbol (*). According to the boxplot obtained, there is no indication of an outlier.

f) Use the Interquartile range to determine whether 62 is an outlier or not. Explain.

From part b) and c), the interquartile range (IQR) is 25.25 and the five number summary includes: Minimum Q1 Median Q3 Maximum 18.00 29.50 37.00 54.75 62.00

( . * , . * ) ( . . * . , . . * . ) . , .1 31 5 1 5 29 50 1 5 25 25 54 75 1 5 25 25 8 375 92 625Q IQR Q IQR

Since 62 belongs to the interval . , .8 375 92 625 , it is not an outlier.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

14

***Enter the number of hours worked before Christmas in Column 1 and enter the number of hours worked after Christmas in Column 2.

Step 1. Select Data>Stack>Columns.

Step 2. Double click each column in Stack the following columns:

Check Column of current worksheet and type the name Hours. Type Group in Store subscripts in option. Check Use variable names in subscript column.

Click OK.

The data in columns C1 and C2 are stacked in C3 Hours

and C4 has codes that identify the hours as “Before” or “After”.

4. The data shown here represent the number of hours that 12 part-time employees at a toy store worked during the weeks before and after Christmas. Compare two distributions using descriptive statistics and boxplots.

Before 38 16 18 24 12 30 35 32 31 30 24 35

After 26 15 12 18 24 32 14 18 16 18 22 12

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

15

Step 3. Click on Stat>Basic Statistics>Display Descriptive Statistics.

Step 4. Double click C3 Hours for the Variables and double click C4 Group for By variables.

Step 5. Click Graphs…, then check Boxplot of data. Click OK.

Step 6. Click OK.

The boxplots are displayed in the graph window. The

boxplot shows that the employees worked more hours before Chrsitmas than after Christmas. Also, the range and variability of the distribution of hours are greater before Christmas.

The descriptive statistics for hours

worked for before and after Christmas are displayed in the session window.

Group

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

16

***Enter the weights of 25 soccer players in Column 1. a) Construct a stem and leaf plot.

Step 1. Click on Graph>Stem-and-Leaf.

Step 2. Click on the inside of the Graph variables and double click “C1 Weight”

You have the option of checking Trim outliers if the exercise requires you to do so.

Step 3. Click OK.

is displayed n the session window.

5. Following are the weights of 25 soccer players:

144 162 197 173 183 129 209 190 117 160 179 177 154 132 151 159 175 154 148 166 184 157 162 150 136

a) Construct a stem and leaf plot b) Construct a boxplot c) Comment on the shape of the distribution. Should the sample mean or the sample median be used as the center of measurement? d) Calculate the sample mean and median. e) Change the first entry from 144 to 1444. (This type of mistake often occurs when

entering data. The outlier of 1444 is a mistake.) Using the modified data set that includes the outlier, calculate the mean and median.

f) The mean and median are two common ways to measure the “center” of a set of data. Which one is more affected by outliers?

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

17

Step 2. Click on Graph Variables and double click “Weight”

Step 3. Click OK.

The boxplot is displayed in the graph window.

c) Comment on the shape of the distribution. Should the sample mean or the sample median be used as the center of measurement?

Even though the distribution is slightly skewed, it is still very close to a bell shaped curve.

Since the shape of the distribution is bell shaped, the mean would be more appropriate to use as the center of measurement.

Weight 210200190180170160150140130120

18

Step 1. Click on Stat>Basic Statistics>Display Descriptive Statistics.

Step 2. Click on the Variable box and double click “C1 Weight”

Step 3. Click Statistics and check option boxes for Mean and Median.

*Uncheck other options. Click OK

Step 4. Click OK.

The results are displayed in the session window.

The sample mean value is 161.92. The sample median is 160.00.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

19

e) Change the first entry from 144 to 1444. (This type of mistake often occurs when entering data. The outlier of 414 is a mistake.) Using the modified data set that includes the outlier, calculate the mean and median.

***Change the first entry from 144 to 1444.

Follow the same procedures in part d) and obtain the

the following results.

The new sample mean value is 213.9. The new sample median value is 162.0.

f) The mean and median are two common ways to measure the “center” of a set of data. Which one is more affected by outliers?

As it is shown in part e) the mean is more affected by outliers.

1. Type in all the blood types in column C1 of the worksheet. A B B AB O O O B AB B B B O A O A O O O AB AB A O B A

a) Make a Categorical Frequency Table b) Construct a Pareto chart c) Construct a pie graph.

CChh22 FFrreeqquueennccyy DDiissttrriibbuuttiioonnss aanndd GGrraapphhss && CChh33 DDaattaa DDeessccrriippttiioonn

***Enter the given data into C1 and name the column Blood Type.

a) Making a Categorical Frequency Table

Step 1. Select Stat>Tables>Tally Individual Values

Step 2. Double-click C1 in the Variables list

Step 3. Check the boxes for the statistics: Counts, Percents, and Cumulative percents.

Step 4. Click OK

session window.

2

b) Construct a Pareto chart Step 1. Click on Stat > Quality Tools > Pareto Chart

Step 2. Click the option to Chart defects data in, and double click “C1 Blood Type”

Step 3. Click OK

The pareto chart is displayed in the graph window.

Note: The cumulative percent chart will disappear by doing the following: Step 1. Click on Stat > Quality Tools > Pareto Chart >Options… Step 2. Click “Do not chart cumulative percent” option

Step 3. Click OK

C ou

8 7 4 4 Percent 34.8 30.4 17.4

ABABO

25

20

15

10

5

0

100

80

60

40

20

0

o un

8 7 4 4 Percent 34.8 30.4 17.4

ABABO

9

8

7

6

5

4

3

2

1

0

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

3

C) Construct a Pie chart Step 1. Click on Graph>Pie Chart.

Step 2. Click on the inside of the Categorical Variables box, double click “C1 Blood Type”

Step3. Click on Labels> Slice Labels Choose Category name and Percent Check “Draw a line from label to slice”

Click OK.

34.8% O

30.4% B

17.4% AB

17.4% A

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

4

a) Open the worksheet file containing the data from Example 2-2, the high temperature for the 50 states (page 39).

Step1. Click File> Open Worksheet

Step 2. Choose the minitab_portable-datasets folder.

Step 3. Select “E c02-S02-02”

Note: Be sure to choose Minitab Portable[*.mtp] as the Files of type.

Step 4. Click Open.

The data (high temperature for 50 states) is copied in a new

worksheet.

b) Construct a Histogram which displays 7 classes with the class

2. Graph for Quantitative Data a) Open the worksheet file containing the data from Example 2-2, the high temperature for the 50 states (page 39). b) Construct a histogram which displays 7 classes with the class width 5. Use 99.5 as the first lower class boundary. c) Construct a frequency polygon. d) Construct an ogive.

E c02- S02- 02 Example Chapter 2 Section 2 Example 2

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

5

width 5. Use 99.5 as the first lower class boundary.

Step 1.Select Graph>Histogram>Simple

Step 2. Click on Graph variables and double click “C1 TEMERATURES”

Step 3. Click Scale… Select the Gridlines tab. Check Y major ticks and X major ticks.

Select the Y-Scale Type tab. Check Frequency

Click OK.

Step 4. Click Labels. Type the title -Record High Temperature

Type Your name and Date in the footnotes Click OK.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

6

Step 5. Click on Data Options. Click the tab for Group Options. Uncheck both options.

Click OK.

window.

The Edit Scale dialgoue is displayed.

Step 8. Click the tab for Binning, then the option for Cutpoint.

Click the button for Midpoint/Cutpoint positions.

Type in the textbox: 99.5:134.5/5. This is the shortcut for entering the sequence of 99.5 to 134. 5 by 5. These are boundaries for each class.

Step 9. Click OK.

graph window.

7

Class boundaries X(Class Midpoint) Frequency 99.5–104.5 10 2 104.5–109.5 107 8 109.5–114.5 112 18 114.5–119.5 117 13 119.5–124.5 122 7 124.5–129.5 127 1 129.5–134.5 132 1

c) Construct a Frequency Polygon Step 1. Select File>New>Minitab Worksheet.

Step 2. Enter the midpoints of each class in C1 and the corresponding frequencies in C2. Use one midpoint higher (i.e. 137) and lower (i.e. 97). They will be needed to anchor the endpoints.

Step 3. Select Graph>Scatterplot>With Connect line.

Step 4. Double click “C1 f” for Y variables and “C1 X” for X-variables.

Step 5. Click Data View, then the Data Display tab. Check two options: Symbols and Connect line. Click OK.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

8

Step 6. Click Scale. Click the tab for Gridlines then check the major ticks for X and Y.

Click the tab for Reference Lines then type 0 for the Y positions.

Click OK twice.

window.

The Edit Scale dialgoue is displayed.

In the Scale tab, click the option for Positions of ticks. Type 97:137/5

Click OK.

X

f

140130120110100

20

15

10

5

0

9

The ogive (cumulative frequency graph) can be constructed by

following the steps for a frequency polygon with two minor changes:

Step 1. Make the following changes in the worksheet.

Change the X values to the class limits from 99.5 to 134.5 by 5. Change the frequencies to cumulative frequencies.

Step 2. Select Graph>Scatterplot>With Connect line.

Step 3. Click Labels. Change the title. – Ogive of Record High Temperatures.

Step 4. Click OK.

Step 5. Double click on the x-scale.

The Edit Scale dialgoue is displayed.

In the Scale tab, click the option for Positions of ticks. Type 99.5:134.5/5

Click OK.

X

f

134.5129.5124.5119.5114.5109.5104.599.5

50

40

30

20

10

Your Name Date

Your Name Date

10

***Enter the given data and name the column Sit Ups.

a) Construct a stem and leaf plot. Step 1. Click on Graph>Stem-and-Leaf.

Step 2. Click on the inside of the Graph variables and double click “C1 Sit Ups”

You have the option of checking Trim outliers if the exercise requires you to do so.

Step 3. Click in the Increment text box, and enter 10 (the class width).

Step 4. Click OK.

The stem and leaf plot is displayed in the session

window

3. The maximum numbers of sit-ups completed by the participants in an exercise class after 1 month in the program are recorded:

24 31 54 62 36 28 37 55 18 27 58 32 37 41 55 39 56 42 29 35

a) Construct a stem and leaf plot. b) Calculate the sample mean and sample standard deviation. c) Find the five-number summary. d) Construct a boxplot e) Identify any outlier(s) obtained from the boxplot. f) Use the Interquartile range to determine whether 62 is an outlier or not. Explain.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

11

Step 1. Click on Stat>Basic Statistics>Display Descriptive Statistics.

Step 2. Click on the Variable box and double click “C1 Sit Ups”

Step 3. Click Statistics and check option boxes for Mean, Standard deviation, Variance, First quartile, Median, Third quartile, Interquartile range, Minimum, Maximum, and N nonmissing.

*Uncheck other options. Click OK

Step 4. Click OK.

The results are displayed in the session window.

The sample mean value is 39.80. The sample standard deviation is 12.76.

c) Find the five-number summary.

Follow the same procedures in part b) and obtain the

five-number summary.

Minimum Q1 Median Q3 Maximum 18.00 29.50 37.00 54.75 62.00

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

12Sit Ups 6050403020

Boxplot of Sit Ups

d) Construct a boxplot Step1. Click on Graph>Boxplot Click OK to select simple box plot.

Step 2. Click on Graph Variables and double click “C1 Sit Ups”

Step 3. Click on Data View and check Interquartile range box and Outlier symbols in the data display

menu.

The boxplot is displayed in the graph window.

Note: The boxplot can be transposed horizontally. Step 1. Double click the horizontal edge of the box frame

Step 2. Check “Transpose value and category scales in the Edit Scale.

Step 3. Click OK.

13

e) Identify any outlier(s) obtained from the boxplot. Values beyond the whiskers are outliers and it is indicated by the asterisk symbol (*). According to the boxplot obtained, there is no indication of an outlier.

f) Use the Interquartile range to determine whether 62 is an outlier or not. Explain.

From part b) and c), the interquartile range (IQR) is 25.25 and the five number summary includes: Minimum Q1 Median Q3 Maximum 18.00 29.50 37.00 54.75 62.00

( . * , . * ) ( . . * . , . . * . ) . , .1 31 5 1 5 29 50 1 5 25 25 54 75 1 5 25 25 8 375 92 625Q IQR Q IQR

Since 62 belongs to the interval . , .8 375 92 625 , it is not an outlier.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

14

***Enter the number of hours worked before Christmas in Column 1 and enter the number of hours worked after Christmas in Column 2.

Step 1. Select Data>Stack>Columns.

Step 2. Double click each column in Stack the following columns:

Check Column of current worksheet and type the name Hours. Type Group in Store subscripts in option. Check Use variable names in subscript column.

Click OK.

The data in columns C1 and C2 are stacked in C3 Hours

and C4 has codes that identify the hours as “Before” or “After”.

4. The data shown here represent the number of hours that 12 part-time employees at a toy store worked during the weeks before and after Christmas. Compare two distributions using descriptive statistics and boxplots.

Before 38 16 18 24 12 30 35 32 31 30 24 35

After 26 15 12 18 24 32 14 18 16 18 22 12

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

15

Step 3. Click on Stat>Basic Statistics>Display Descriptive Statistics.

Step 4. Double click C3 Hours for the Variables and double click C4 Group for By variables.

Step 5. Click Graphs…, then check Boxplot of data. Click OK.

Step 6. Click OK.

The boxplots are displayed in the graph window. The

boxplot shows that the employees worked more hours before Chrsitmas than after Christmas. Also, the range and variability of the distribution of hours are greater before Christmas.

The descriptive statistics for hours

worked for before and after Christmas are displayed in the session window.

Group

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

16

***Enter the weights of 25 soccer players in Column 1. a) Construct a stem and leaf plot.

Step 1. Click on Graph>Stem-and-Leaf.

Step 2. Click on the inside of the Graph variables and double click “C1 Weight”

You have the option of checking Trim outliers if the exercise requires you to do so.

Step 3. Click OK.

is displayed n the session window.

5. Following are the weights of 25 soccer players:

144 162 197 173 183 129 209 190 117 160 179 177 154 132 151 159 175 154 148 166 184 157 162 150 136

a) Construct a stem and leaf plot b) Construct a boxplot c) Comment on the shape of the distribution. Should the sample mean or the sample median be used as the center of measurement? d) Calculate the sample mean and median. e) Change the first entry from 144 to 1444. (This type of mistake often occurs when

entering data. The outlier of 1444 is a mistake.) Using the modified data set that includes the outlier, calculate the mean and median.

f) The mean and median are two common ways to measure the “center” of a set of data. Which one is more affected by outliers?

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

17

Step 2. Click on Graph Variables and double click “Weight”

Step 3. Click OK.

The boxplot is displayed in the graph window.

c) Comment on the shape of the distribution. Should the sample mean or the sample median be used as the center of measurement?

Even though the distribution is slightly skewed, it is still very close to a bell shaped curve.

Since the shape of the distribution is bell shaped, the mean would be more appropriate to use as the center of measurement.

Weight 210200190180170160150140130120

18

Step 1. Click on Stat>Basic Statistics>Display Descriptive Statistics.

Step 2. Click on the Variable box and double click “C1 Weight”

Step 3. Click Statistics and check option boxes for Mean and Median.

*Uncheck other options. Click OK

Step 4. Click OK.

The results are displayed in the session window.

The sample mean value is 161.92. The sample median is 160.00.

Math 227 Elementary Statistics-Minitab Handout Ch2 and Ch3

19

e) Change the first entry from 144 to 1444. (This type of mistake often occurs when entering data. The outlier of 414 is a mistake.) Using the modified data set that includes the outlier, calculate the mean and median.

***Change the first entry from 144 to 1444.

Follow the same procedures in part d) and obtain the

the following results.

The new sample mean value is 213.9. The new sample median value is 162.0.

f) The mean and median are two common ways to measure the “center” of a set of data. Which one is more affected by outliers?

As it is shown in part e) the mean is more affected by outliers.