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 : 1 12 12 8 5 6 3 9 3 6

Book 2 : 3 3 2 4 6 4 5 4 5 4

Find the range for book 1. Range equals

Find the range for book 2. Range

Find the standard deviation for book 1.

Sample standard deviation

(Do not round until the final answer. Then round to one decimal place as​ needed.)

Answer 1

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

Xi = length of ith word for Book 1 and Yi = length of ith word for Book 2 and n = number ob observation.

Now we find the Range and Sample Standard Deviation for both the book.

Formula:

=> Range = (Maximum Value - Minimum Value) and ,

Calculation:-

Table for Calculation:

1	3	-5.5	-1	30.25	1
12	3	5.5	-1	30.25	1
12	2	5.5	-2	30.25	4
8	4	1.5	0	2.25	0
5	6	-1.5	2	2.25	4
6	4	-0.5	0	0.25	0
3	5	-3.5	1	12.25	1
9	4	2.5	0	6.25	0
3	5	-3.5	1	12.25	1
6	4	-0.5	0	0.25	0
Total=65	Total=40	-	-	Total=126.5	Total=12

[ Note:

and,

]

Calculation for Book 1:

Maximum word length for Book 1 = 12 and Minimum word length for Book 1 = 1

So, Range = ( Maximum word length - Minimum word length ) = ( 12-1 ) = 11

Sample Standard Deviation is given by,

[ putting the value from table and we get ]

[round to one decimal places]

Calculation for Book 2:

Maximum word length for Book 2 = 6 and Minimum word length for Book 2 = 2

So, Range = ( Maximum word length - Minimum word length ) = ( 6-2 ) = 4

Sample Standard Deviation is given by,

[ putting the value from table and we get ]

[round to one decimal places]

Compare of two sets of results:-

In statistics, we know that Range and Standard Deviation both are Dispersion Measure.

Since standard deviation is a measure of spread, so larger standard deviation indicates that data are more spread out where small standard deviation indicates that data are less spread out. For this problem sample standard deviation of Book 1 is greater than sample standard deviation of Book 2. So we get, word length of Book 1 are more spread out and word length of Book 2 are less spread out. Here we also see that range of Book 1 is greater than range of Book 2. So range also indicates that word length of Book 1 are more spread out and word length of Book 2 are less spread out.

Conclusion:-

Yes, there appear to be a difference in variation.