Chapter 1.2, Problem 57E

(a)

To determine

To make: a histogram of the distribution.

Answer to Problem 57E

  

Explanation of Solution

Given:

  

Calculation:

The Histogram of percentage of words with 1 to 15 letters is below:

  

The shape is regular and skewed towards right. The skewness towards right means that majority of words have letters between to 7 but several words have letters between 7 and 15. It is Unimodal with one peak at 3.

The center of data is at 4 letters.

The spread is 14 from 1 letter to 15 letters. There are no outliers or extreme values in the data.

Conclusion:

“Therefore, a histogram of the distribution is made.

Shape: regular and skewed towards right.

Center: 4 letters.

Spread: 14 from 1 letter to 15 letters.”

(b)

To determine

To find: how the distribution of lengths of words are used

Answer to Problem 57E

Short words (2,3 and 4 letters) are used maximum times.

Explanation of Solution

The distribution of the percentage of words with 1 to 15 letters as compare to the distribution of lengths of words used in Shakespeare's plays, in particular at short words (2,3 and 4 letters are used maximum times. In the case of long words (more than 10 letters) are using as low as between 1% to 4%.

Length:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Percent:	3.6	14.8	18.7	16	12.5	8.2	8.1	5.9	4.4	3.6	2.1	0.9	0.6	0.4	0.2