Explanation Definition: 1. While computing the mean of a frequency distribution, write all products x ⋅ f of the values and their frequencies in a new column of the table. Represent the sum of these products by ∑ ( x ⋅ f ) . Denote the sum of the frequencies by ∑ f . The mean is then ∑ ( x ⋅ f ) ∑ f . 2. If x is a data value in a set whose mean is x ¯ , then x − x ¯ is called x’s deviation from the mean. 3. We denote the standard deviation of a sample of n data values by s = ∑ ( x − x ¯ ) 2 n − 1 . 4. We calculate the standard deviation, s, of a sample that is given as a frequency distribution as s = ∑ ( x − x ¯ ) 2 ⋅ f n − 1 . Here f is the frequency of data value x , and n = ∑ f is the number of data values in the distribution. Calculation: First find the mean of the given data set. To compute the mean, let us find all products x ⋅ f of the given values and their respective frequencies. For x = 4 and f = 2 , the product x ⋅ f = 4 ⋅ 2 = 8. For x = 5 and f = 0 , the product x ⋅ f = 5 ⋅ 0 = 0. For x = 6 and f = 3 , the product x ⋅ f = 6 ⋅ 3 = 18. For x = 7 and f = 5 , the product x ⋅ f = 7 ⋅ 5 = 35. For x = 8 and f = 4 , the product x ⋅ f = 8 ⋅ 4 = 32. For x = 9 and f = 5 , the product x ⋅ f = 9 ⋅ 5 = 45. For x = 10 and f = 1 , the product x ⋅ f = 10 ⋅ 1 = 10. The sum of these products is 8 + 0 + 18 + 35 + 32 + 45 + 10 = 148. Therefore, ∑ ( x ⋅ f ) = 148. The sum of the frequencies is 2 + 0 + 3 + 5 + 4 + 5 + 1 = 20. Therefore, ∑ f = 20. Therefore, the third column of the given table is as below. Number, x Frequency, f Product, x ⋅ f 4 2 8 5 0 0 6 3 18 7 5 35 8 4 32 9 5 45 10 1 10 ∑ f = 20 ∑ x ⋅ f = 148 The mean is then ∑ ( x ⋅ f ) ∑ f = 148 20 = 7

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Chapter 14.3, Problem 12E

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The mean and standard deviation and complete the table for the number of job offers made to graduates of a Microsoft network administrator

To find: The mean and standard deviation and complete the table for the number of job offers made to graduates of a Microsoft network administrator

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The mean and standard deviation and complete the table for the number of job offers made to graduates of a Microsoft network administrator