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M119L06-page10

M119L06-page10 - values are distributed To avoid confusion...

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(Lesson 6: Measures of Spread or Variation; 3-3) 3.24 Observe that this is higher than 10.2 points, the SD from Example 1. The “tilted” average we used in Step 4 inflated our value for the sample SD. Many calculators have an s or σ n 1 button that allows you to compute the sample SD of inputed data. PART E: APPLICATIONS If the population SD of a data set is 10.2 points, what is the usefulness of that? If we have different populations (for example, men and women) for which the same measure (such as age or height using the same units) is being taken, then we could compare their SDs. In Parts F, G, and H , we will use the SD to provide information about how data
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Unformatted text preview: values are distributed. To avoid confusion, let’s say we’re dealing with the population SD of a population data set. PART F: CHEBYSHEV’S THEOREM Chebyshev’s Theorem Let k be a real number such that k > 1 . What fraction of the values in a data set must lie within k SDs of the mean? The answer is: at least 1 − 1 k 2 . Pro: This theorem applies to any distribution shape and is thus distribution free. Con: 1 − 1 k 2 might not be close to our desired fraction; it only provides a lower bound on what the desired fraction could be....
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