Explanation Definition: 1. The range of a data set is the difference between the largest and smallest data values in the set. 2. If a data set contains n data values, the mean x ¯ of the data set is x ¯ = ∑ x n . 3. If x is a data value in a set whose mean is x ¯ , then x − x ¯ is called x’s deviation from the mean. 4. We denote the standard deviation of a sample of n data values by s = ∑ ( x − x ¯ ) 2 n − 1 . 5. We calculate the standard deviation, s, of a sample that is given as a frequency distribution as s = ∑ ( x − x ¯ ) 2 ⋅ f n − 1 . Here f is the frequency of data value x , and n = ∑ f is the number of data values in the distribution. Calculation: First find the range of the given data set. The largest data value is 6 and the smallest data value is 4. Since range is the difference between the largest and the smallest data value, the range of given data is 6 − 4 = 2. Next find the mean of the given data set. Begin by finding the sum of the given data. Sum of 4, 6, 4, 6, 4, 6, 4, and 6 is 40. There are 8 values in the given data. Therefore, the mean is x ¯ = 40 8 = 5. Now find the standard deviation. Observe that there are some repeated values in the given data. Therefore, we will use a frequency table to compute the standard deviation. The frequency of 4 is 4. That is, 4 comes four times in the data set. Similarly, the frequency of 6 is 4. Now find the product x ⋅ f for each data value. Notice that 4 ⋅ 4 = 16 , and 6 ⋅ 4 = 24. The deviation is the difference between each product value and the mean. Therefore, the deviation of 4 from the mean 5 is 4 − 5 = − 1

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ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Chapter 14.3, Problem 10E

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To find:

The range, mean, and standard deviation for the following data set:

4, 6, 4, 6, 4, 6, 4, 6

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Chapter 14.3, Problem 9E

Chapter 14.3, Problem 11E

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The range, mean, and standard deviation for the following data set: 4, 6, 4, 6, 4, 6, 4, 6

Solution Summary: The author explains that the range of a data set is the difference between the largest and smallest data values.

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To find: The range, mean, and standard deviation for the following data set: 4, 6, 4, 6, 4, 6, 4, 6

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Chapter 14 Solutions

To find:

The range, mean, and standard deviation for the following data set:

4, 6, 4, 6, 4, 6, 4, 6