Chapter 8 Section 3

# Chapter 8 Section 3 - 8.3 Measures of Dispersion In this...

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8.3 Measures of Dispersion In this section, you will study measures of variability of data.  In addition to being able to find measures of central  tendency for data, it is also necessary to determine how  “spread out” the data. Two measures of variability of data  are the  range   and the  standard deviation

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Measures of variation Example 1. Data for 5 starting  players from two basketball  teams: A: 72 , 73, 76, 76, 78 B: 67, 72, 76, 76, 84  Verify that the two teams  have the same mean heights,  the same median and the  same mode.
Measures of Variation Ex. 1 continued. To describe the difference in the two data  sets, we use a descriptive measure that indicates the  amount of spread , or dispersion, in a data set.   Range :  difference between maximum and  minimum  values of the data set.

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Measures of Variation Range of team A:  78-72=6 Range of team B: 84-67=17 Advantage of range: 1) easy to compute Disadvantage: only two values are considered .
Unlike the range, the sample standard deviation takes into account all data values. The following procedure is used to find the sample standard deviation: 1. Find mean of data  :  =    = 1 n i x n 72 73 76 76 78 75 5 + + + + =

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Step 2: Find the deviation of each score from the mean x 72 72-75 = -3 73 73–75 = -2 76 76-75 = 1 76 76-75 = 1 78 78-75= 3 Note that the  sum of the  deviations = 0  0 - = ( ) 0 x x - x x
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Chapter 8 Section 3 - 8.3 Measures of Dispersion In this...

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