M119L05 - (Lesson 5: Measures of Center; 3-2) 3.01 CHAPTERS...

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(Lesson 5: Measures of Center; 3-2) 3.01 CHAPTERS 3: DESCRIPTIVE STATISTICS II LESSON 5: MEASURES OF CENTER (SECTION 3-2) PART A: FOUR MEASURES Example 1 The five students in a class take a test. Their scores in points are as follows: 80 76 100 83 100 How can we find a single number that tells us how well the class did? Let’s look at four possibilities for measuring the center of a data set. 1) [Arithmetic] Mean or Average There are other measures called means, but the arithmetic mean (or simply “the mean”) is by far the most common. In Our Example Mean = Sum of all data values Number of values = 80 + 76 + 100 + 83 + 100 5 = 439 5 = 87.8 points Warning : You must group or compute (“process”) the numerator before dividing by 5. You can do this by either placing grouping symbols like parentheses around the numerator, or by pressing “ENTER” or the like on your calculator before dividing. What would be wrong with entering the following on your calculator: 80 + 76 + 100 + 83 + 100 ÷ 5 = ? Remember to write units, such as “points”, in your final answer where appropriate.
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(Lesson 5: Measures of Center; 3-2) 3.02 Notes on Rounding : • In Chapter 3 , we will typically round off our final answers to one more decimal place than the number of decimal places provided in the given data. In this Example, because the given data values are integers (rounded off to zero decimal places), we round off our final answers to one decimal place. • Avoid rounding intermediate results, however. This becomes an issue in later sections. Triola suggests rounding off intermediate results to at least twice as many decimal places as will be present in your final answer, but this might not be enough. Always read instructions on exams. They take precedence over everything. 2) Median If N is odd, the median is the data value in the middle position after sorting the data in increasing or decreasing order. In Our Example 80 76 100 83 100 We must first sort the five data values. 76 80 83 100 100 ± The median is 83 points. Observe that there are as many data values below the median (2) as above. (If two or more data values equal the median, this might not be the case.)
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(Lesson 5: Measures of Center; 3-2) 3.03 If N is even, the median is the average of (i.e., the midpoint between) the two data values in the two middle positions after sorting the data. Modified Example Let’s say there were only four test scores: 80 76 100 83 We must first sort them. 76 80 83 100 ± ± The two middle values are 80 and 83, so we take their average, 80 + 83 2 = 81.5 . The median is 81.5 points. 3) Mode The mode is the most frequent data value, if any, in the data set. A data set could have no mode, one mode, or more than one mode. It is sometimes denoted by
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M119L05 - (Lesson 5: Measures of Center; 3-2) 3.01 CHAPTERS...

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