Chapter 3 Notes

Chapter 3 Notes - WEEK 3: MEASURES OF CENTER Complete this...

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WEEK 3: MEASURES OF CENTER Complete this guide on your computer as you read. In the previous chapter we analyzed data frequency distribution, but here we are interested in the values that the data set tends to center around (CENTRAL TENDENCY), discrepancies within the data set or changes over time (VARIATION) and the position of a specific value within a set (RELATIVE STANDING). Read chapter 3 as you complete your class notes. To check to see if you understand the concepts you can check your Student’s Solution Manual for the odd numbered examples. Your TH3 assignment will incorporate some of the examples used in the class notes. 3.2 MEASURES OF CENTER MEAN The most well known central measure of tendency is the mean (also informally known as the average). The formula for the mean is shown below. x x n = NOTE: 1. The symbol x represents the mean. 2. Each x represents a single data element. 3. The Σ x means to sum up all the data elements. 4. The n represents the total number of data elements So, the formula says to add up all the individual data elements and divide that sum by the number of elements. If you have the data elements [3,4,5,6] for example, the sum would be 3+4+5+6 =18; the n would be 4 and the mean would be 18/4 = 6 3-2-5 Find the mean of 53,52,75,62,68,58,49,49. Use a calculator and show your work. x x n = Σ x = n = Σ x/n = x = 3-2-6 Find the mean of 3,24,30,47,43,7,47,13,44,39. Use a calculator. Show your work. x x n = Σ x = n = Σ x/n = x = Is the cereal sugar content MEAN representative of American consumption? Why? 1
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MEDIAN Another well known central measure of tendency is the median which is the middle value after the data elements are sorted from lowest to highest. Example 1 - Find the median of 3 4 1 2 9 2 8. First, sort the data from lowest to highest: 1 2 2 3 4 8 9 Then, since 3 is the middle element, so the median of the set of data is 3 . Notice that this is not an average, but just the number in the middle of the set. Now we will add another element to our original set to give us an even number of points. Example 2 - Find the median of 3 4 1 2 9 2 8 5. First we sort the data: 1 2 2 3 4 5 8 9. Find the middle TWO values 3 4 Now, find the mean of those values. x = (3 + 4) / 2 = 7/2 = 3.5. The median of the set of data is now 3.5 So, to find the median of a set of data with an odd number of elements, sort the data and locate the middle number. For data with an even number of elements, sort the data, locate the two middle numbers, and then, find the mean of those two numbers. 3-2-5 Find the median of 53,52,75,62,68,58,49,49. Reorder the data: Median numbers: Average of median numbers: 3-2-6 Find the median of 3,24,30,47,43,7,47,13,44,39. Reorder the data:
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This note was uploaded on 04/14/2009 for the course STAT stat 200 taught by Professor Mosekim during the Spring '09 term at Wisconsin.

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Chapter 3 Notes - WEEK 3: MEASURES OF CENTER Complete this...

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