You have a friend who is an aspiring author of children’s books. To increase her

Question

You have a friend who is an aspiring author of children’s books.  To increase her chances of getting her books published, she wants to know how many pages her books should have.  At the local library, she counts the number of pages in a random selection of children’s picture books.   Here are the data:

34 30 29 32 52 25 24 27 31 29 24 26 30 30 30 29 21 30 25 28 28 28 29 38 28 29 24 24 29 31 30 27 45 30 22 16 29 14 16 29 32 20 20 15 28 28 29 31 29 36

a. What length book would represent the lowest third (33rd percentile) of the selected sample of children’s books?

b. The first draft of your friend’s next book would have 37 pages when printed.  Is this an unusually long children’s picture book?  In other words, assuming that the sample she reviewed in the library was representative, what proportion of children’s books would be longer than this one?

Explanation / Answer

Given data sorted in increasing order is

14,15,16,16,20,20,21,22,24,24,

24,24,25,25,26,27,27,28,28,28,

28,28,28,29,29,29,29,29,29,29,

29,29,29,30,30,30,30,30,30,30,

31,31,31,32,32,34,36,38,45,52

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(a)

For the 33rd percentile,

R = 33/100 x (50 + 1) = 51/3 = 17

From the above sorted data, no. of pages with rank = 17 is 27.

So, Length of book which would represent the lowest third (33rd percentile) of the selected sample of children’s books is 27 pages.

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(b)

Total no. of books reviewed = 50

No. of books with more than 37 pages = 3

Proportion of books with more than 37 pages = 3/50 = 0.06

So, it would be considered an unusually long children's picture book.

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