Chapter 1: Q. 83. (page 53)

The histogram shows the distribution of the percent of women aged 15 and over who have never married in each of the 50 states and the District of Columbia. Which of the following statements about the histogram is correct?
a. The center (median) of the distribution is about 36%.
b. There are more states with percentages above 32 than there are states with percentages less than 24.
c. It would be better if the values from 34 to 50 were deleted on the horizontal axis so there wouldn’t be a large gap.
d. There was one state with a value of exactly 33%.
e. About half of the states had percentages between 24% and 28%.

Short Answer

Expert verified

The correct option is (e)

e. About half of the states had percentages between 24% and 28%.

Step by step solution

Given information.

The histogram shows the distribution of the percent of women aged 15 and over who have never married in each of the 50 states and the District of Columbia.

Step 1. Which of the following statements about the histogram is correct

(a) The statement is incorrect because it claims that the centre of the distribution is at 36%, but there are no bars above 36% in the histogram.

(b) The statement is incorrect because there are fewer states with percentages greater than 32 than states with percentages less than 24 (the opposite of the given statement), because the two bars to the right of 32 in the histogram are much shorter than the two bars to the left of 24.

(c) The statement is incorrect because deleting values on the horizontal axis that are between some bars of the histogram would give the impression that the data did not contain an outlier (because there would no longer be any gaps in the histogram), whereas the bar centred at 51 is clearly an outlier (as it is separated from the other bars by a large gap).

(d) The statement is incorrect because there is a bar at 33% with height 1, which corresponds to data values ranging from 32% to 34%, and thus the one state represented by this bar could correspond to any value ranging from 32% to 34%. (not necessarily exactly 33 percent )

(e) The statement is correct because the histogram's highest bars are between 24 and 28 percent. These bars have frequencies of 14 and 10 respectively (frequency is the height of the bar). This corresponds to 14+10=24 of the 50 states, or roughly half of the states.

As a result:

(e) In approximately half of the states, the percentage of women over the age of 15 who have never married ranges between 24 and 28 percent.