Explanation Given: The frequency distribution mentioned is, Class Frequency, F 500–999 sq. ft 13 1,000–1,499 sq. ft 9 1,500–1,999 sq. ft 11 2,000–2,499 sq. ft 7 2,500–2,999 sq. ft 5 Formula used: Mean for grouped data: M e a n ( x ¯ ) = Sum of ' product , F M ' n In the formula, F denotes the frequency, M denotes the midpoint and n is the number of values in the set. Standard deviation for grouped data: Standard deviation ( s ) = sum of F ( M − x ¯ ) 2 n − 1 In the formula, F denotes the frequency, M denotes the midpoint, x ¯ denotes the mean, ( M − x ¯ ) denotes the deviation from the mean and n is the number of values in the set. Calculation: The midpoint is calculated by taking the average of the upper endpoint and lower end point of the class. For the first class, 500–999 sq. ft the midpoint is, 500 + 999 2 = 749.5 Similarly for all the remaining classes the midpoints are calculated. The extended table for calculating standard deviation is, Class (in square feet) Frequency, F Midpoint, M Product, FM ( M − x ¯ ) ( M − x ¯ ) 2 F ( M − x ¯ ) 2 500–999 13 749

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ISBN: 2818440003295

Author: CARMAN

Publisher: PEARSON CP

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Chapter 12.3, Problem 1BE

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