Week 2 of Notes
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This 3 page Class Notes was uploaded by Christian Anthony on Wednesday January 13, 2016. The Class Notes belongs to 220 at James Madison University taught by Mr. Greg Jansen in Winter 2016. Since its upload, it has received 77 views. For similar materials see Elementary Statistics in Math at James Madison University.
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Date Created: 01/13/16
STATS 220 1/20 Mean- The sum of all of your set of numbers divided by the number of numbers you have. In other words, add up all of your numbers and divide by how many numbers you started with. The formula for the mean is: This is a very complex way of saying add up your numbers, divide them by how many you had. This picture is your two different kinds of means. Population is too complex to discern on your own, so it should be given to you. The difference of the two was not given in the lecture. Median- The middle number, numerically, of a given set of numbers. ● To find the mean, you must arrange the numbers given into numerical order (smallest number to largest number.) ● Find “n”, which is the amount of numbers you have. ○ If “n” is odd, the median is in the “n+1 over 2” position. This means you must take n, add 1, and divide that by 2. ○ If “n” is even, it is in the “average of n over two” position. This is a fancy way of saying take the average of the two middle numbers. *The median is fairly simple to find when you get the hang of it. These technical formulas are only for very large problems. *Median is labeled with a capital M. Example for Median: 1) 97 98 97 51 100 103 107 2) Arrange them in order, least to greatest. 3) 51 97 97 98 100 103 107 Now using n, which is 7 (odd), we determine the median is in the “n+1 over 2” position. So we take n, which is seven, and add 1. Eight. Then divide by two. Four. The fourth position is the fourth number of the set in order, making the answer 98. If this were odd, like below: 97 97 98 100 103 107 Then we would assume the median is in the average of n over 2 position. So we take 6/2 and get 3. Go three positions in, and take the number above and the number below it. This means 98 and 100. Find the average of the two numbers. This makes the median 99. MEANSAND MEDIANSWITHDISCRETEDATA: EXAMPLE:Categories of Hurricanes That Made Landfallon U.S.Soil Category Frequency 1 58 2 36 3 47 4 15 5 2 The above chart isclassified as discrete data.This makes themean and the median hard to discern. In order tofind it, we must realizethat category 1has fifty eight ones. Thismeans, in a numerical list,the beginning would have 58ones. That’s a large number to count through. Instead, wecanuse the formulas. The mean is2.15, if youchoose togothroughusing this formula: (1*58)(2*36)(3*47)(4*15)(5*2) (58+36+47+15+2) *Whiledecimals aren’t allowed in themean,this is an exception due tothe discrete data set. As faras the median, there are158numbers(I’d really justtrust me here…) This means that there isan even number. We can take158and divide itby two, and weget 79. Take that andadd one, like in theformula,and weget80. Now, given thefactthat both of these numbers are twos whenlooked aton a data line,the mean has tobea two. SHAPES AND OUTLIERS: Outliers are associated with the three main shapes we’vegone over. Skewed leftmeans an outlier isto the left, skewedrightmeansan outlier is to the right.If theshape is symmetric,there isnooutlier. *The mean is sensitive tooutliers. It changes drasticallyif one ispresent.Themedianis resistant tothe outlier.These are exactterms used inclass, soI’d suggest knowing them.
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