Stats20Descriptive

Stats20Descriptive - Untitled Document 6/27/09 9:39 PM...

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Unformatted text preview: Untitled Document 6/27/09 9:39 PM Lesson 2.3 Mean, Median and Mode (1) Mean The mean is the same as the average. To find the mean, add all the values and divide by the total number of values. Example: {2, 3, 5, 6} The mean The letter x with a bar over it, , represents the sample mean. The Greek letter, µ , represents the population mean. Median The median is the middle value of a set of numbers that has been ordered from smallest to largest. The upper case letter M is used for the median. Example: A sample of statistics exam scores for 14 students are (in order from smallest to largest) as follows: 53, 59, 63, 63, 72, 72, 76, 78, 81, 83, 84, 84, 90, 93 Notice that 14 is an even number. The median is between 7th and 8th values (the middle two values). The 7th value is 76 and the 8th value is 78. The median M = Example: A second sample of statistics exam scores for 15 students are (in order from smallest to largest) as follows: 52, 60, 65, 67, 70, 71, 74, 76, 78, 78, 78, 80, 86, 89, 95 Notice that 15 is an odd number. The median is the 8th value (the middle value). The 8th value is 76 so the median M = 76. Mode The mode is the most frequent value in the set of numbers. file:///Users/bonk/Desktop/dukeonly/Stats20Descriptive.html Page 1 of 2 Untitled Document 6/27/09 9:39 PM Example: In the data set 52, 60, 65, 67, 70, 71, 74, 76, 78, 78, 78, 80, 86, 89, 95, the most frequent value is 78. The mode = 78. Example: In the data set 52, 53, 53, 53, 60, 67, 72,72,72, 90, both 53 and 72 occur the most number of times (3 times each) so there are two modes, 53 and 72. We call this set of data bimodal meaning it has two modes. Think About It Which is the "best" measure of the center of a set of data ? That all depends on the data. If the data tend toward being different values with no extremely large or small values, the mean might be the best measure of the data. If the data is highly skewed, the median might be the best measure of the center. If the data repeats values, the mode might be the best measure. Example: A shoe store sells women's shoes in sizes 5 through 11. The average shoe size is 7 1/2, the median size is 8 1/2, and most frequent shoe size is 8. Which is the best measure ? Because the most frequent shoe size is 8, the manager orders more shoes in size 8 than any other size. Even though the average shoe size is 7 1/2 and the median is 8 1/2, the mode is the best measure of the center for this particular shoe store. Example: Suppose in a community of 7 households, the yearly income is (in dollars) 50,000; 53,000; 58,000; 59,000; 60,000; 61,000; 5,000,000 The mean is $763,000 and the median is $59,000. Which is the best measure ? The median better represents the center of income of the majority of households. In this case, the median is the better measure of the center of the data. Bibliography (1) Dean, S., Illowsky, B. Elementary Statistics, 2004, http://sofia.fhda.edu/gallery/statistics/lessons/lesson02 - 1.html, under Creative Commons License Deed, © 2004 Foothill- De Anza Community College District & The William and Flora Hewlett Foundation, accessed June 25, 2009. Content Developed by Susan Dean and Barbara Illowsky, Licensed under a Creative Commons License Published by the Sofia Open Content Initiative © 2004 Foothill -De Anza Community College District & The William and Flora Hewlett Foundation file:///Users/bonk/Desktop/dukeonly/Stats20Descriptive.html Page 2 of 2 ...
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