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: From the given table understand the frequency of each data value. x f 72 7 73 1 78 3 84 6 86 2 93 1 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 = 72 and f = 7 , the product x ⋅ f = 72 ⋅ 7 = 504. For x = 73 and f = 1 , the product x ⋅ f = 73 ⋅ 1 = 73. For x = 78 and f = 3 , the product x ⋅ f = 78 ⋅ 3 = 234. For x = 84 and f = 6 , the product x ⋅ f = 84 ⋅ 6 = 504. For x = 86 and f = 2 , the product x ⋅ f = 86 ⋅ 2 = 172. For x = 93 and f = 1 , the product x ⋅ f = 93 ⋅ 1 = 93. The sum of these products is 504 + 73 + 234 + 504 + 172 + 93 = 1580. Therefore, ∑ ( x ⋅ f ) = 1580. The sum of the frequencies is 7 + 1 + 3 + 6 + 2 + 1 = 20. Therefore, ∑ f = 20. The mean is then ∑ ( x ⋅ f ) ∑ f = 1580 20 = 79

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Author: Tom Pirnot

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Chapter 14.3, Problem 19E

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To find:

The mean and standard deviation of the distribution given by the following table:

Score 72 73 78 84 86 93

Frequency 7 1 3 6 2 1

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Chapter 14.3, Problem 18E

Chapter 14.3, Problem 20E

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The mean and standard deviation of the distribution given by the following table: Score 72 73 78 84 86 93 Frequency 7 1 3 6 2 1

Solution Summary: The author explains how to compute the mean and standard deviation of a frequency distribution.

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To find: The mean and standard deviation of the distribution given by the following table: Score 72 73 78 84 86 93 Frequency 7 1 3 6 2 1

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Chapter 14 Solutions

To find:

The mean and standard deviation of the distribution given by the following table:

Score 72 73 78 84 86 93

Frequency 7 1 3 6 2 1