Question

Traveling to work How long do people travel each day to get to work? The following table gives the average travel times to work (in minutes) for workers in each state and the District of Columbia who are at least 16 years old and don’t work at home. 3

Part (a). Make a histogram to display the travel time data using intervals of width 2 minutes, starting at 14 minutes.

Part (b). Describe the shape of the distribution. What is the most common interval of travel times

Short answer

Part (a)

Part (b)

Roughly symmetric

22$<$24

Step-by-step solution

Part (a) Step 1. Given information. 

The following table gives the average travel times to work (in minutes) for workers in each state and the District of Columbia who are at least 16 years old and don’t work at home. 3

Part (a) Step 2. Given information. 

Table of frequencies

First, we'll calculate the frequency of each interval, which is the number of data values that fall within each interval. The first interval begins at 14 and has a width of 2, resulting in 14<16. The next intervals will be 16-<18, 18-<20, and so on until all data values are assigned to exactly one interval.

The frequency is then defined as the number of data values that belong to the class.

Interval	Frequency
14<16	2
16<18	4
18<20	2
20<22	8
22<24	14
24<26	12
26<28	5
28<30	2
30<32	2

Each bar's width must be the same, and the bars must be bounded by interval boundaries, while the height must be equal to the frequency.

Part (b) Step 1. The shape of the distribution. 

The distribution is roughly symmetric because the highest bars are roughly in the middle of the histogram.

The most frequent interval of travel times is 22-$$24.

As a result:

Roughly symmetric

22$<$24