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

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