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 Human Histogram

An Engineering Statistics Lesson
Developed by Teri Rhoads
The University of Oklahoma

Step by Step Instructions

1.

A brief introduction including questions to promote the discussion of probability in every day life is given.  This could include asking students where they see statistics or probability in their day to day lives.  Typical answers focus on probability and include the weather forecasts or lotteries. 
 

2.

Ask students how many believe that there are at least two persons born on the same day in the room and twins or multiple births do not count.  Use a show of hands to determine how many students believe that there will be at least two people born on the same day.  (Note that year does not play a role in this question!)
 

3.

Ask the students to form a human histogram by forming 12 bins based on the months of their birth.  To avoid utter chaos, have students form the histogram one month at a time while you call out the month.  Then, ask the students to order themselves within the bins with the first of the month at the bottom of the bin and the last of the month at the top of the bin.  This allows the students to make the birthday discovery on their own. 

ALTERNATIVE:  If the class is too large use the first 6 months or use a portion of the class for the full 12 months.
 

4.

Once all students are in their bins and ordered, ask the students to identify the people who share the same birthday.  Explain that as long as there is a minimum of 23 persons participating that there was over a 50% chance that two people would share the same birth month and day.  As you do this multiple times, you will find that probability will catch up with you and at some point there will be a time when there are not 2 birthdays.  This is a good learning/teaching experience as well. 
 

5.

Have students count off.  Discuss the median.  Ask for someone to tell you where they think the median is.  Find the actual median using the equations;

Odd – the person’s birthday located at (n+1)/2 or Even – the midpoint between the persons’ birthdays located at n/2 and (n+2)/2.  Have that person raise both hands in the air so that students can physically see the location of the median.
 

6.

Ask for the definition of the mode.  Remind students that another word for mode is maxima and they are looking for the bin with the maximum amount of birthdays in it.  You can discuss bi-modal and tri-modal as well.  Opportunity sometimes knocks with the actual occurrence of one of these situations.
 

7.

Explain that the mean is another measure of central tendency and it would be located where a fulcrum would balance a platform that contained all of the students if weight was the variable we were measuring. 
 

8.

Have the students look around at how the class is distributed between the different months.  Talk about the fact that variation is a measure of the spread of the data.

                                          Lesson   Step by Step Instructions  |   Handouts and Overheads

©1997,  Teri Rhoads.   
These materials may be duplicated for educational purposes if properly credited.

 

 

 

 

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