Question

The following box plot shows the U.S. population for 1990, the latest available year.

a. Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)? How do you know?

b. 12.6% are age 65 and over. Approximately what percentage of the population are working age adults (above age 17 to age 65)?

Short answer

a) The number of children exceed the number of senior persons. The left whisker indicates that children aged 17 and under account for 25% of the population. Adults 50 and older account for 25 percent of the population, so adults 65 and older account for less than 25 percent of the population.

b) Adults of working age account for around $62.4$percent of the population.

Step-by-step solution

Part (a) - Step 1: To determine

a. Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)?

Part (a) - Step 2: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

We are given in the below box plot:

a)The number of children exceed the number of senior persons. The left whisker indicates that children aged 17 and under account for 25% of the population. Adults 50 and older account for 25 percent of the population, so adults 65 and older account for less than 25 percent of the population.

Part (b) - Step 3: To determine

$12.6\%$are age 65 and over. Approximately what percentage of the population are working age adults (above age 17 to age 65)?

Part (b) - Step 4 : Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

We are given in the below box plot:

b) We know that $\$12.6\%$of the population is 65 and up. The lower quartile is 17, thus there will be$75\%$of the population over the age of 17. As a result, about $75\%-12.6\%=62.4\%$of the population will be employed.