meanmedianmode(5)

8/13/2019 meanmedianmode(5)

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Mean, Median, andMode


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In everyday life it is often importantto collect data. Perhaps from a

survey or a questionnaire. Once wehave collected the data, it is thenimportant to arrange it in a waywhich allows someone to analyze theinformation, so that a conclusion ordecision can be made.


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Statistics 3 of the most important statistics weuse when we analyze data are called:

The mean The median

The mode


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The Mean The meanof a set of data is theaverage. To find the mean, add all

the data values together and divideby the number of values.


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Lets start with an easy

example! In her last 5 games, Sara has scoredthe following number of points:

12, 16, 11, 17, and 18 What is the mean of these scoring

totals?


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To determine the mean, all we haveto do is add up all of her points

and then divide by the number ofgames she played

12+16+11+17+18=74

74/5=14.8 Saras scoring mean was 14.8 points

per game


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The Median The medianis the middle value afterthe data has been arranged in order.

If the set of data contains an evennumber of values, then the median isthe average (the mean) of the twomiddle values.


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Lets try a couple of

these! Jake received the following testgrades on his last 7 quizzes:

79, 88, 75, 71, 89, 80, 92 What was his median grade?


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First, we must arrange the scores

in order.71, 75, 79, 80, 88, 89, 92

In this case, we have 7 values and because7 is an odd number, we have a middle

number. The middle value will be the 4thnumber from either end of the set. In thiscase the median would be 80. 71, 75, 79, 80, 88, 89, 92

The median of this set is 80


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Lets do one with an even

number of data values Over an 8 day period, Bessie, thecow, produced the following total

gallons of milk per day: 16, 18, 19, 15, 14, 20, 17, 22

What was the median number of

gallons over this period of time?


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Again, the first step is to arrange the values inorder 14, 15,16,17,18,19,20,22

This time we have an even number of values, thatmeans there is no value exactly in the middle. So,we have to find the average of the two middlenumbers.

14, 15,16,17,18,19,20,22

I have underlined the two middle numbers To average, we simply add them together and thendivide by 2

17+18=35 35/2=17.5

The median of this set is 17.5 gallons.


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The Mode The modeis the data value that appearsthe most in the set. Because no value mayappear more often than any other, it is

possible for a set to have no mode. Andbecause it is possible for a set to containmore than one element which appears thesame number of times as another, it is

possible for a set to have more than onemode.


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Lets look at a couple of

examples The following is a list of heights (ininches) of a high school basketball

team: 68,67,66,70,74,72,68,71,75,68,72,71

What is the mode?


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To determine the mode, all wehave to do is find which data

values appear the most 68, 67, 66, 70, 74, 72, 68, 71, 75, 68,

72, 71

There are 2-71s and 2-72s BUT, there are 3-68s

So, the mode is 68!


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Lets look at one more This is a list of the grades of a classon a recent math test:

85, 78, 90, 91, 88, 85, 73, 84, 90, 95,67, 70

Find the mode for this set of data.


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If you write the numbers in order,you will clearly see any multiple

entries. 67, 70, 73, 78, 84, 85, 85, 88, 90,

90, 91, 95

This set has 2 modes: 85 and 90

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