Explanation Given: The set of numbers mentioned is 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8 Formula used: Mean: Mean = sum of the data values number of data values Range: Range = largest data value − smallest data value Standard deviation: Standard deviation ( s ) = sum of ( x − x ¯ ) 2 n − 1 In the formula, x ¯ denotes the mean, ( x − x ¯ ) denotes the deviation from the mean and n is the number of values in the set. Calculation: Range: The set of numbers is 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8. In this set the smallest value is 2 and the largest value is 8. Substitute 8 for the ‘largest data value’ and 2 for the ‘smallest data value’ in the range formula. Range = 8 − 2 = 6 Thus, the value of range is 6 _ . Standard deviation: The set of numbers is 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8. The number of data values is 10. That is n = 10 . Add all the data values for ‘sum of data values’ and substitute 10 for ‘number of data values’ in the mean formula. Mean ( x ¯ ) = 5 + 4 + 2 + 5 + 7 + 5 + 2 + 4 + 3 + 8 10 = 45 10 = 4.5 The deviation from the mean and square of deviation is, Numbers ( x − x ¯ ) ( x − x ¯ ) 2 5 ( 5 − 4.5 ) = 0.5 ( 0.5 ) 2 = 2.5 4 ( 4 − 4.5 ) = − 0.5 ( − 0.5 ) 2 = 2.5 2 ( 2 − 4

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ISBN: 2818440003295

Author: CARMAN

Publisher: PEARSON CP

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Chapter 12.3, Problem 1AE

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The range and the standard deviation for set of numbers 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8.

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Chapter 12.3, Problem 2LC

Chapter 12.3, Problem 2AE

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The range and the standard deviation for set of numbers 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8.

Solution Summary: The author calculates the range and standard deviation for the set of numbers 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8.

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The range and the standard deviation for set of numbers 5, 4, 2, 5, 7, 5, 2, 4, 3 and 8.

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