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# Histograms

## Visual representation of data on a histogram and the many graphs associated with this display

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Practice Histograms

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Avoiding a Traffic Jam

Look at the traffic going north-south in the picture above and compare it with the much emptier roads going east-west. Did the traffic engineers miss something? How did they know how much traffic to expect?

#### Why It Matters

Traffic jams waste thousands of hours for workers, and highway traffic and safety engineers try very hard to prevent them from happening. In order to determine how much traffic a new road has to carry, engineers set up counting machines that record the number of cars traveling on the existing roads. The design of anything always depends on how it is going to be used; the picture below, for instance, shows some ways in which we count, in various applications.

The traffic engineers need to know how many vehicles are currently using the road. The problem is that this number is different at different times of the day and on different days of the year. For example, the traffic at 6 a.m. is different from the traffic at 8 a.m., because at 8 a.m. everybody is trying to get to work. In order to accommodate all these variations, engineers spend a year measuring how many vehicles pass in every hour, and they organize this information into frequency tables and histograms. By analyzing these traffic measurements, they can determine the number of lanes the new road will need to have.

#### Explore More

An engineer planning a new road has observed that four o’clock in the afternoon is the busiest time. Below is a frequency diagram that shows how the 4 p.m. traffic varies over the course of a week. You can see that on Thursdays, there are more than 7,000 vehicles using the road in one hour.

If one lane can carry 3,000 cars per hour, the engineer has to decide whether she should construct two lanes or three. If she decides on three, there will never be a traffic jam, but the cost will be very high because more lanes are expensive. Her alternative is to plan for two lanes, which works for six out of seven days, but makes the Thursday drive a little slower.

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