Susan interviewed the twenty five students in her class, as - PowerPoint Presentation

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Susan interviewed the twenty five students in her class, asking each person how often they eat out.  Most students replied between zero and three times.  However, one student reported eating out for every single meal (21 meals a week).  Data: 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3,

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, 1, 1, 0, 3, 1, 2, 2Which measure of central tendency will best convey how often the students typically eat out?Possible Answers: Mean, Median, or Mode

The ScenarioSlide4

Mean

: The arithmetic average. Add up all of the values and divide by the number of scores.

Mean = 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3, 21, 1, 1, 0, 3, 1, 2, 2 25

= 57 meals ‘eaten out’ 25 students = 2.28 meals ‘eaten out’ per student

MeanSlide5

Consider what the mean would be

without the outlier

…Mean = 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3, 1, 1, 0, 3, 1, 2, 2 24

=

36 meals eat out 24 students = 1.5 meals ‘eat out’ per studentMeanSlide6

College Student Income

US Dollars

(in thousands)MeanSlide7

US Dollars

(in thousands)

MeanCollege Student IncomeSlide8

US Dollars

(in millions)

MeanCollege Student IncomeSlide9

US Dollars

(in millions)

Based on the Mean… College Students are Millionaires!Mean

MeanSlide10

Mean

– Uses all data, but is

sensitive to outliersMeanSlide11

Mode

: The most frequently occurring value

ModeSlide12

Mode

: The most frequently occurring value

Modes: 1, 2

ModeSlide13

Mode

: The most frequently occurring value

Mode: 0

Mode

A small change in frequency can affect the mode(s)Slide14

Mode

: The most frequently occurring value

Mode: 0

Mode

A small change in frequency can affect the mode(s)

Students Don’t Typically Eat OutSlide15

Mode

– Perhaps the least robust. Easily affected by small changes in frequency

ModeSlide16

Median

: The middle value in a ranked distribution. If there are an even number of values, then take the average of the middle two values.

MedianSlide17

Median

: The middle value in a ranked distribution. If there is an even number of values, then take the average of the middle two values.

Raw Data: 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3, 21, 1, 1, 0, 3, 1, 2, 2

MedianSlide18

Median

: The middle value in a ranked distribution. If there is an even number of values, then take the average of the middle two values.

Raw Data: 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3, 21, 1, 1, 0, 3, 1, 2, 2

Ranked

: 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 21MedianSlide19

Median

: The middle value in a ranked distribution. If there is an even number of values, then take the average of the middle two values.

Raw Data: 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3, 21, 1, 1, 0, 3, 1, 2, 2

Ranked

: 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 21MedianSlide20

Median

: The middle value in a ranked distribution. If there is an even number of values, then take the average of the middle two values.

Raw Data: 2, 0, 1, 0, 2, 2, 1, 0, 0, 2, 1, 3, 3, 3, 2, 1, 3, 21, 1, 1, 0, 3, 1, 2, 2

Ranked

: 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 21Median: 2MedianSlide21

US Dollars

(in millions)

MeanMean

Based on the Mean… College Students are Millionaires!Slide22

US Dollars

(in millions)

Median

Median

Based on the Median… College Students as a Group Aren’t WealthySlide23

US Dollars

(in millions)

MedianBased on the Median… College Students as a Group Aren’t Wealthy

MedianSlide24

Median

– Does not use all data,

but is robust; not affected by outliersMedianSlide25

Measures of Central Tendency – And Outliers

When there is an outlier, which measure of central tendency

can we generally count on to give us the best measure of what is typical?

Which measure should Susan report?Slide26

Measures of Central Tendency – And Outliers

When there is an outlier, which measure of central tendency

can we generally count on to give us the best measure of what is typical?

Which measure should Susan report?

Mean – Uses all data, but sensitive to outliersSlide27

Measures of Central Tendency – And Outliers

When there is an outlier, which measure of central tendency

can we generally count on to give us the best measure of what is typical?

Which measure should Susan report?

Mean

– Uses all data, but

sensitive to outliers

Mode

– Easily affected by small

changes in frequencySlide28

Measures of Central Tendency – And Outliers

When there is an outlier, which measure of central tendency

can we generally count on to give us the best measure of what is typical?

Which measure should Susan report?

Mean – Uses all data, but sensitive to outliersMode

– Easily affected by small

changes in frequency

Median

– Does not use all data,

but is robustSlide29

Real World Use

When there is an outlier, your reporting options are to report:

Median, or Median and MeanMeasures of Central Tendency – And OutliersSlide30

Real World Use

When there is an outlier, your reporting options are to report:

Median, or Median and MeanMeasures of Central Tendency – And OutliersIf you think the outlier does not belong in thedata set (i.e., was an error)… then consider also reporting the mean without the outlier.Slide31

Posted on

Flickr as fast food is the best! by Ebruli. Available under Creative Commons Attribution 2.0 Generic License to share and remix.Posted on Wikimedia Commons as Earth Western Hemisphere white background by Hansjorn. Available in the Public Domain.ReferencesSlide32

References

Posted on

 Flickr as Money! by Tracy O. Available under Creative Commons Attribution-Share Alike 2.0 Generic License to share and remix.Posted on Wikimedia Commons as Bill Gates 2004 crop. Originally posted to Flickr by deVos. Available under Creative Commons Attribution-Share Alike 2.0 Generic License to share and remix.Slide33

Appendix: Online Resources

Mean, Median, and Mode Song

From LearningUpGrade.com; posted on YouTube.Description of Video: A basic overview of how to determine the mean, median and mode. Includes music and animation.

Length: 1m 33s

.View at tinyurl.com/yfsnmh9Comparing the Properties of the Mean and the Medianat Principles & Standards for School Mathematics Description of this Interactive Demonstration: Move the numbers around on the number line, and see the corresponding effect on the mean and median. How do outliers affect the mean and median?

Length: Interactive Demonstration

Participate at

tinyurl.com/33tngrSlide34

Appendix: Online Resources

Statistics: The Average

Posted by khanacademy on YouTube. Description of Video: A more in depth, college level, introduction to the mean, median, and mode. Note – starts with a blank screen, which is then written upon…

Length:

12m 35sView at tinyurl.com/ykbbvmjIt’s Not Hard (Averages Song)

Posted on YouTube by

jalapenojane

.

Description of Video

: This is just for fun…. Covers mean, median, and mode in a way that may leave you laughing aloud.

Length: 3m 49s

View at

tinyurl.com/yhc885wSlide35

Appendix: Creative Commons License

Creative Commons Attribution-Share

Alike 3.0 LicenseYou are free to share (copy, distribution and transmit the work) and to remix (to adapt the work) this

Powerpoint

Presentation What to Report When There is an Outlier by Robert G. Kelley, Ph.D. on the condition that you provide attribution (you must attribute the work in a manner specified by the author or licensor – but not in any way that suggests that they endorse you use of the work) and share alike (if you alter, transform, or build upon this work, you may distribute the resulting work only under the same, similar or compatible license) this work.Note that the online resources listed in the appendix are separate works from this Powerpoint presentation, and are not covered by this Creative Commons License.Please attribute this work to:

Robert G. Kelley, Ph.D. (www.miracosta.edu/home/rkelley)