GED Mathematical Reasoning: Histograms

Histograms are like frequency tables and line plots in that they show how frequently a data value occurs within a data set. But a histogram looks very different than a frequency table or line plot. A histogram is a type of bar graph that displays frequencies – it shows how many times a data value falls into a certain interval. 

Let’s look at an example.

Suppose Marketa is considering opening a lunch café near the local community college. She is interested in finding out the demand for a lunchtime eatery in the area, so she visits campus one afternoon and asks passersby how many times per month they eat off-campus on their lunch break. This frequency table and histogram represent the results of her survey.

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Notice that the histogram provided in this example has a horizontal axis running along the bottom which represents the number of times people eat out for lunch, in intervals of 5. The horizontal axis is also called the x-axis. The vertical axis, also known as the y-axis, represents the frequencies – the number of responses that fall within each of those intervals.

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Do you see the relationship between the frequency table and the histogram?

Looking at the frequency table, we see that 30 people surveyed responded that they each lunch out between 6 and 10 times per month. On the histogram, we see that the bar representing the interval 6 to 10 along the horizontal x-axis has a height corresponding to 30 on the vertical y-axis.

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Looking at the histogram we can see that – overall – the responses Marketa received indicate that people each lunch out anywhere between 1 and 25 times per month.

The highest concentration of responses fell between 6 and 20 times per month, since those three bars on the histogram are the tallest.

The most frequent answer was between 16 and 20 times per month, since that bar is the tallest on the histogram. That means that of those surveyed, the most popular answer people gave was that they eat out for lunch between 16 and 20 times per month.

Another type of histogram you may come across is one that displays percentages, instead of frequencies, along the vertical y-axis. Here is another version of Marketa’s histogram that does just that.

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In this modified histogram, each bar represents the PERCENT of responses that fall within each interval, which can be found by dividing the frequency of each interval by the total number of responses.

Say, for instance, Marketa would like to use the percentage histogram to determine the percent of responses that fell between 6 and 20 times per month.

First, she would approximate the percent of responses in each interval: 6 to 10, 11 to 15, and 16 to 20. These percentages will be based on the height of each bar.stats34

Based on the height of each bar over the intervals 6 to 10, 11 to 15 and 16 to 20, the percentages are approximately: 25%, 22% and 41% respectively.

25% + 22% + 41% = 88%

Therefore 88% of those surveyed eat lunch out between 6 and 20 times per month.

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