Explanation Given: The frequency distribution mentioned is, Class Frequency, F 0–1.9 sec 4 2.0–3.9 sec 6 4.0–5.9 sec 9 6.0–7.9 sec 10 8.0–9.9 sec 8 10.0–11.9 sec 7 12.0–13.9 sec 6 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, 0–1.9 sec the midpoint is, 0 + 1.9 2 = 0.95 Similarly for all the remaining classes the midpoints are calculated. The extended table for calculating standard deviation is, Class Frequency, F Midpoint, M Product, FM ( M − x ¯ ) ( M − x ¯ ) 2 F ( M − x ¯ ) 2 0–1

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ISBN: 9780135902028

Author: SAUNDERS

Publisher: PEARSON

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The standard deviation of the grouped data for a frequency distribution

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