Explanation Given: The set of numbers mentioned is 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1. 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 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1. In this set the smallest value is 2.5 and the largest value is 20.1. Substitute 20.1 for the ‘largest data value’ and 2.5 for the ‘smallest data value’ in the range formula. Range = 20.1 − 2.5 = 17.6 Thus, the value of range is 17.6. Standard deviation: The set of numbers is 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1. The number of data values is 9. That is n = 9 . Add all the data values for ‘sum of data values’ and substitute 9 for ‘number of data values’ in the mean formula. Mean ( x ¯ ) = 19.9 + 2.5 + 19.8 + 5.6 + 12.4 + 7.1 + 7.6 + 9.3 + 20.1 9 = 114.3 9 = 12.7 The deviation from the mean and square of deviation is, Numbers ( x − x ¯ ) ( x − x ¯ ) 2 19.9 ( 19.9 − 12.7 ) = 7.2 ( 7.2 ) 2 = 51.84 2.5 ( 2.5 − 12.7 ) = − 10.2 ( − 10

Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)

11th Edition

ISBN: 9780134756967

Author: Hal Saunders, Robert Carman

Publisher: PEARSON

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Chapter 12.3, Problem 2AE

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The range and the standard deviation for set of numbers 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1.

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Chapter 12.3, Problem 1AE

Chapter 12.3, Problem 3AE

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Chapter 12 Solutions

Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)

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The range and the standard deviation for set of numbers 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1.

Solution Summary: The author calculates the range and standard deviation for the set of numbers 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1.

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The range and the standard deviation for set of numbers 19.9, 2.5, 19.8, 5.6, 12.4, 17.1, 7.6, 9.3 and 20.1.

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