Explanation Given: The frequency distribution is, Class Frequency, F 22–26 ft 4 27–31 ft 7 32–36 ft 11 37–41 ft 9 42–46 ft 5 47–51 ft 2 Procedure used: Steps for constructing the frequency distribution: 1. Defined the classes using the class width. 2. For each of the class place the tally marks, if the data value is in the class interval. 3. Count the number of tally marks for each class interval for obtaining frequency. Steps for finding mean of grouped data: 1. Calculate the midpoint by finding the mean of the endpoints of the class. This is denoted by M . 2. Multiply the each of the frequency F with the corresponding midpoint M for each of the class. These values are denoted as ‘Product, FM ’. 3. Calculate the sum of the frequencies which is denoted as n . 4. Calculated the sum of ‘Product, FM ’. Divide the sum of ‘Product, FM ’ with the sum n . Calculation: Mean for grouped data: Class Frequency, F Midpoint, M Product, FM ( M − x ¯ ) ( M − x ¯ ) 2 F ( M − x ¯ ) 2 22–26 4 24 96 –11.3 127.69 510.76 27–31 7 29 203 –6.3 39.69 277.83 32–36 11 34 374 –1.3 1.69 18.59 37–41 9 39 351 3.7 13.69 123.21 42–46 5 44 220 8.7 75

11th Edition

ISBN: 9780135902028

Author: SAUNDERS

Publisher: PEARSON

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Chapter 12, Problem 2EPS

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The mean and the standard deviation of the grouped data

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The mean and the standard deviation of the grouped data

Solution Summary: The author explains the procedure used for constructing the frequency distribution.

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The mean and the standard deviation of the grouped data

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