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Measures of central tendency Dominique Warmsley & Bettina Bonsu March 29, 2010 Math 300-003
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When you hear someone use the word “average” to describe a set of numbers, there are 3 ways you can describe data, all of which can be thought of as “measures of central tendency” 1. Mean 2. Median 3. Mode
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Mean: A set of numbers is the sum of values divided by the number of values. We can write this as a formula. Example: These are the values 5 + 10 + 7+ 12 + 8 + 6= 48 Add all the numbers Then count all the values and then divide by number of values. 48 divided by 6 = 8 So the mean for this set of values is 8
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Work It out! What is the Mean of this set 7,10, 8, 14, 6 Remember: follow all the steps!
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Answer is: 7 + 10 + 8 + 14+ 6= 45 45 divided by 5 is ……… 9 So your mean is 9
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Median: a middle number of a set of numbers. You have to make sure your numbers are in order first. Values need to be ordered least to greatest. If the number of data values in the list is odd, then the median is the middle number in the list. If the number of data value is even, there is no single middle number . So the median is the mean of the 2 middle numbers in the list.
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Watch Me!!! Example: 35, 74, 53, 98, 32, Place in order least to greatest 32, 35, 53, 74, 98 The median is 53 There are 5 values (an odd #), so the median is the middle number.
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Now I’ll watch you! 4200, 3600, 4500, 3500, 3800 Now put them in order, and find your median
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See it wasn’t that hard The order least to greatest 3500, 3600, 3800, 4200, 4500 Because there are five data values (an odd number) the middle number is median. 3800 is the median. But you knew that right.
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It can also look like this ….. 2600, 3900, 9800, 2200, 4100, 1500 Next step is least to greatest 1500, 2200, 2600, 3900, 4100, 9800 The middle # are….. 2600, 3900 you add both numbers 2600 + 3900 = 6500 Then 6500 divided by 2 = 3250 Remember these steps…….
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Now you can try this ….. Find the median of this value set: 26.08, 39.02, 98.07, 22.03, 41.04, 15.02
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Solution….. Find the median of this value set: 26.08, 39.02, 98.07, 22.03, 41.04, 15.02 In order from smallest to largest: 15.02, 22.03, 26.08, 39.02, 41.04 ,98.07 Taking the mean of the middle two values 26.08 + 39.02= 65.1 65.1 divided by 2= 32.55
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Mode: set of a value that occur most often. If two values occur most often we say the data is a bimodal. If more than two values occur most often, we say there is no mode.
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Data Sets Example1: 6.3, 12.5, 2.3, 6.3, 1.2, 3.3, 6.3, The data value 6.3 appears more often then any number . Therefore 6.3 is the mode. Example 2: 2, 12, 14, 67, 98, 6, 15, 13, 10 No data value occurs most often, There is no mode for this set.
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Now you can try this ….. Find the mode of the value sets : Pink, blue, silver, yellow, pink , blue , pink 6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2 2, 5, 10, 3, 6, 19, 11, 20, 19
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Solution…… Find the mode of the value sets : Pink, blue, silver, yellow, pink , blue , pink Mode is: pink 6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2 Bimodal sets are: 6, 14 2, 5, 10, 3, 6, 9, 11, 20, 19 Mode is: none
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Food For Thought! So, remember when you think average, think a set a numbers . And revisit your friends : Mean Median Mode Remember math is your friend ! Give him a hug
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