The line plot is a useful graph for examining small sets of data. It’s especially helpful as a device for learning basic statistical ideas. But for larger data sets, it can be awkward to create, since for each data value there is a corresponding dot. That’s a lot of dots for data sets with hundreds or thousands of values! You can, however, replace a line plot with a frequency bar graph.

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Let’s look at the transition from line plot to frequency bar graph.

We start with the line plot we’ve been using. Remember that the number of dots over each value on the horizontal axis corresponds to the frequency of that data value:

Now remove the dots, and add a vertical scale that indicates the frequency of each value on the horizontal scale:

Problem E1

Complete the table above. Give decimals to three decimal places and percentages to the nearest tenth of a percent.

Notice that the relative frequencies expressed as fractions add up to 17/17, which equals 1. The relative frequencies expressed as decimals also sum to 1, and the relative frequencies expressed as percentages add up to 100%. The total of the relative frequencies expressed as decimals, however, may not always be exactly 1 due to round-off error; they will occasionally add to 1.002 or 0.997, for example, or something very close to 1. Accordingly, the total percentage may not sum to exactly 100%. To decrease round-off error, we would have to increase the number of decimal places used when rounding.

A relative frequency bar graph looks just like a frequency bar graph except that the units on the vertical axis are expressed as percentages. In the raisin example, the height of each bar is the relative frequency of the corresponding raisin count, expressed as a percentage: See Note 9, below.

In this video segment, meteorologist Kim Martucci demonstrates how she solves the statistical problem of predicting the weather. Watch this segment after you have completed Session 2.

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What are Kim Martucci’s strategies for predicting the weather? How are they similar to your strategies for counting raisins? How are they different?

You can find the first part of this segment on the session video approximately 23 minutes and 3 seconds after the Annenberg Media logo. The second part of this segment begins approximately 24 minutes and 48 seconds after the Annenberg Media logo.