Explanation Definition: Mean: It is the ratio of sum of all the data values in a dataset to the total number of data values. The mean is usually denoted by x ¯ . If x is set of data values and n is the total number of data values, then mean is calculated by the formula x ¯ = ∑ x n Measures of dispersion: Range: The range of the given random sample is difference between the largest data value and the smallest data value. Variance: It is defined as ratio of sum of the squares of deviation from the mean to one less than the number of samples in frequency distribution or dataset. It is denoted by s 2 , if x is the random sample and x ¯ is the mean then variance for a random sample is found by s 2 = ∑ ( x − x ¯ ) 2 n − 1 Standard deviation: Standard deviation is the square root of the variance denoted by s = s 2 Steps to find Standard deviation: Step 1: Determine the mean of the set of numbers. Step 2: Subtract the mean from each number in the set and Square each of these differences. Step 3: Find the sum of the squares of the differences. Step 4: Divide this sum by one less than the number of pieces of data. This gives the variance of the sample. Step 5: Take the square root of the variance. This is the Standard deviation of the sample. Calculation: Given dataset is x = ( 79 , 90 , 95 , 95 , 96 ) . Number of data values or samples n = 5 . Now, let’s find the range of the dataset as shown below. Range = Largest data value − smallest data value Range = 96 − 79 Range = 17 Steps to calculate variance: Step 1: Calculate mean of the dataset. Mean of dataset is calculated as shown below: x ¯ = ∑ x n x ¯ = ( 79 + 90 + 95 + 95 + 96 ) 5 x ¯ = 455 5 = 91 mean = 91 Step 2: Calculate Square of the deviation from the mean. Scores Square of the deviation from mean x ( x − x ¯ ) 2

13th Edition

ISBN: 9780357325865

Author: SMITH

Publisher: CENGAGE L

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Chapter 14.2, Problem 27PS

To determine

To find:

The range and the standard deviation (correct to two decimal places).for the random sample

79, 90, 95, 95, 96.

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Chapter 14.2, Problem 26PS

Chapter 14.2, Problem 28PS

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Chapter 14 Solutions

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The range and the standard deviation (correct to two decimal places).for the random sample 79 , 90 , 95 , 95 , 96 .

Solution Summary: The author explains how to find the range and standard deviation of a random sample.

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To find:

The range and the standard deviation (correct to two decimal places).for the random sample

79, 90, 95, 95, 96.

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Chapter 14 Solutions

The range and the standard deviation (correct to two decimal places).for the random sample 79 , 90 , 95 , 95 , 96 .

Solution Summary: The author explains how to find the range and standard deviation of a random sample.

Concept explainers

Videos

To find: The range and the standard deviation (correct to two decimal places).for the random sample 79, 90, 95, 95, 96.

Want to see the full answer?

Chapter 14 Solutions

To find:

The range and the standard deviation (correct to two decimal places).for the random sample

79, 90, 95, 95, 96.