Chapter_02

# Chapter_02 - Chapter 2 Describing Distributions with...

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BPS - 5th Ed. Chapter 2 1 Chapter 2 Describing Distributions with Numbers

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BPS - 5th Ed. Chapter 2 2 Numerical Summaries Center of the data mean median Variation range quartiles (interquartile range) variance standard deviation
BPS - 5th Ed. Chapter 2 3 Mean or Average Traditional measure of center Sum the values and divide by the number of values ( 29 x n x x x n x n i i n = + + + = = 1 1 1 2 1

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BPS - 5th Ed. Chapter 2 4 Median ( M ) A resistant measure of the data’s center At least half of the ordered values are less than or equal to the median value At least half of the ordered values are greater than or equal to the median value If n is odd , the median is the middle ordered value If n is even , the median is the average of the two middle ordered values
BPS - 5th Ed. Chapter 2 5 Median ( M ) Location of the median: L(M) = (n+1)/2 , where n = sample size. Example : If 25 data values are recorded, the Median would be the (25+1)/2 = 13 th ordered value.

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BPS - 5th Ed. Chapter 2 6 Median Example 1 data: 2 4 6 Median ( M ) = 4 Example 2 data: 2 4 6 8 Median = 5 (ave. of 4 and 6) Example 3 data: 6 2 4 Median 2 ( order the values: 2 4 6 , so Median = 4 )
BPS - 5th Ed. Chapter 2 7 The mean and median of data from a symmetric distribution should be close together. The actual (true) mean and median of a symmetric distribution are exactly the same. In a skewed distribution, the mean is farther out in the long tail than is the median [the mean is ‘pulled’ in the direction of the possible outlier(s)].

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BPS - 5th Ed. Chapter 2
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Chapter_02 - Chapter 2 Describing Distributions with...

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