The lengths of the first 10 words of 2 books are listed below. Find the range an

Question

The lengths of the first 10 words of 2 books are listed below. Find the range and standard deviation for each of the two samples, then compare the two sets of results. Does there appear to be a difference in variation? Book 1: 6 1 2 6 6 11 10 7 10 4 Book 2: 2 3 4 5 5 2 3 3 2 4 Find the range for book 1. Range = letters Find the range for book 2. Range = letters Find the standard deviation for book 1. Sample standard deviation = letters (Do not round until the final answer. Then round to one decimal place as needed.) Find the standard deviation for book 2. Sample standard deviation = letters (Do not round until the final answer. Then round to one decimal place as needed.) Is there a difference in variation between the two books?

Explanation / Answer

Consider book 1,

maximum value = 11 Minimum value = 1

so,

Range = Max - Min = 11 - 1 = 10

Similarly, consider book 2,

Range = Max - Min = 5 - 2 = 3

Hence,

The range for book 1 is :

Range = 10

The range for book 2 is

Range = 3

By thumb rule of range,

For book 1,

Standard deviation = Range/4 = 10/4 = 2.5

For book 2,

Standard deviation = Range/4 = 3/4 = 0.75

Observe that, there is difference in variation between the two books.

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