Explanation Given Information: The scores are 85, 73, 74, 69, 87, 81, 68, 76, 78,75, 88, 85, 67, 83, 82, 95, 63, 84, 78, 96, 67, 63, 59, 100, 90, 100, 90, 100, 94, 79, 79, 74. Formula used: General rules for choosing interval: 1) Number of intervals should be between 6 and 20. 2) Length of interval should be same and should always be an odd number. 3) Mid-point should have same number of digits and it should lie between the interval. 4) Lower limit should be lower than the least value and upper limit should be greater than highest value. Mid-point is given by: mid-point = lower limit+upper limit 2 Mean of frequency distribution is given by: Mean = Sum of ( x f ) f Where, x is the mid-point and f is the frequency. Sample standard deviation is given by: s = sum of D 2 f n − 1 Calculation: Consider the scores 85, 73, 74, 69, 87, 81, 68, 76, 78,75, 88, 85, 67, 83, 82, 95, 63, 84, 78, 96, 67, 63, 59, 100, 90, 100, 90, 100, 94, 79, 79, 74. The lowest limit should be lower than 59 and highest limit should be greater than 100. And the intervals should not be less than 6 and should not exceed 20. Check the difference of highest value and lowest value and set the interval accordingly. Here the difference between the highest and lowest value is 41. Now let the number of intervals to be chosen is 6. Now the nearest number that is divisible by 6 is 42. Now the length of interval should be will be ( 42 ÷ 6 ) = 7 . Since the interval difference is taken 42 that is one greater than 41, therefore lowest limit should be 0.5 lower than 59 and upper limit should be greater than 100 by 0.5. interval x f xf 58.5-65.5 65.5-72.5 72.5-79.5 79.5-86.5 86.5-93.5 93.5-100.5 3 5 9 7 3 6 In order to complete the table: Find the mid-point and product of x and f : mid-point ( x ) = lower limit+upper limit 2 = 58.5 + 65.5 2 = 124 2 = 62 product of x and f : x f = x ⋅ f = 62 ⋅ 3 = 186 Find mid-point and product of x and f for all other intervals similarly

11th Edition

ISBN: 9781285199191

Author: Dale Ewen, C. Robert Nelson

Publisher: Cengage Learning

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Chapter 15.9, Problem 2E

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To calculate: The frequency distribution of the following scores from a mathematics test and use it to find the sample standard deviation of the score.

85, 73, 74, 69, 87, 81, 68, 76, 78,75, 88, 85, 67, 83, 82, 95, 63, 84, 78, 96, 67, 63, 59, 100, 90, 100, 90, 100, 94, 79, 79, 74

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Chapter 15 Solutions

Elementary Technical Mathematics

Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E

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The frequency distribution of the following scores from a mathematics test and use it to find the sample standard deviation of the score. 85, 73, 74, 69, 87, 81, 68, 76, 78,75, 88, 85, 67, 83, 82, 95, 63, 84, 78, 96, 67, 63, 59, 100, 90, 100, 90, 100, 94, 79, 79, 74

Solution Summary: The author calculates the frequency distribution of the following scores from a mathematics test and uses it to find the sample standard deviation of score.

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To calculate: The frequency distribution of the following scores from a mathematics test and use it to find the sample standard deviation of the score. 85, 73, 74, 69, 87, 81, 68, 76, 78,75, 88, 85, 67, 83, 82, 95, 63, 84, 78, 96, 67, 63, 59, 100, 90, 100, 90, 100, 94, 79, 79, 74

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Chapter 15 Solutions

To calculate: The frequency distribution of the following scores from a mathematics test and use it to find the sample standard deviation of the score.

85, 73, 74, 69, 87, 81, 68, 76, 78,75, 88, 85, 67, 83, 82, 95, 63, 84, 78, 96, 67, 63, 59, 100, 90, 100, 90, 100, 94, 79, 79, 74