Data Mode!

The following activity about the "mode" of a data set is a great instructional opportunity in the classroom.  It offers an opportunity to teach students mathematical language and activities can be integrated in the classroom to show this in real life situations.  Students can use day of birth and find the mode day within their class or even in a few classes.  They could also pick random numbers from a bag and arrange themselves so that to show the mode and in subsequent lessons the median and mean.  This lesson will set them up well for future lessons on statistical data.

Problem:	The number of points scored in a series of football games is listed below. Which score occurred most often?
	7,  13,  18,  24,  9,  3,  18
Solution:	Ordering the scores from least to greatest, we get:
	3,  7,  9,  13,  18,  18,  24
Answer:	The score which occurs most often is 18.
This problem really asked us to find the mode of a set of 7 numbers.

Definition:

The mode of a set of data is the value in the set that occurs most often.

In the problem above, 18 is the mode. It is easy to remember the definition of a mode since it has the word most in it. The words mode and most both start with the lettersmo. Let's look at some more examples.

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Example 1:	The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode?
	8,  11,  9,  14,  9,  15,  18,  6,  9,  10
Solution:	Ordering the data from least to greatest, we get:
	6,  8,  9,  9,  9,  10,  11  14,  15,  18
Answer:	The mode is 9.

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Example 2:	In a crash test, 11 cars were tested to determine what impact speed was required to obtain minimal bumper damage. Find the mode of the speeds given in miles per hour below.
	24,  15,  18,  20,  18,  22,  24,  26,  18,  26,  24
Solution:	Ordering the data from least to greatest, we get:
	15,  18,  18,  18,  20,  22,  24,  24,  24,  26,  26
Answer:	Since both 18 and 24 occur three times, the modes are 18 and 24 miles per hour. This data set is bimodal.

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Example 3:	A marathon race was completed by 5 participants. What is the mode of these times given in hours?
	2.7 hr,  8.3 hr,  3.5 hr,  5.1 hr,  4.9 hr
Solution:	Ordering the data from least to greatest, we get:
	2.7,  3.5,  4.9,  5.1,  8.3
Answer:	Since each value occurs only once in the data set, there is no mode for this set of data.

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Example 4:	On a cold winter day in January, the temperature for 9 North American cities is recorded in Fahrenheit. What is the mode of these temperatures?
	-8,  0,  -3,  4,  12,  0,  5,  -1,  0
Solution:	Ordering the data from least to greatest, we get:
	-8,  -3,  -1,  0,  0,  0,  4,  5,  12
Answer:	The mode of these temperatures is 0.

Let's compare the results of the last two examples. In Example 3, each value occurs only once, so there is no mode. In Example 4, the mode is 0, since 0 occurs most often in the set. Do not confuse a mode of 0 with no mode.

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Summary:

The mode of a set of data is the value in the set that occurs most often. A set of data can be bimodal. It is also possible to have a set of data with no mode.

Lesson from Math Goodies Website http://www.mathgoodies.com/lessons/vol8/mode.html