GED Mathematical Reasoning: Line Plots

  • A line plot displays the same kind of information as a frequency table, just in a more visual way using a number line. Instead of using tallies, a dot or “x” is placed above the number line to represent each data value.

 

Example 1

Twenty people were surveyed and asked: “How many times do you exercise per week?” Their responses are displayed on the line plot below.  Use the line plot to answer the following questions.

  1. Which answer has the highest frequency?
  2. What is the range?
  3. Are there any outliers?

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Before we complete this example, let’s talk about the relationship between line plots and frequency tables. To illustrate how a line plot relates to a frequency table, here is the same information given in the example’s line plot, but in the form of a frequency table.

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Do you see the relationship between the “x’s” on the line plot and the tallies in the frequency table? Where there is 1 “x” over the answer of zero on the line plot, there is one tally in the frequency table for zero times per week. Where there are 2 “x’s” over the answer one on the line plot, there are 2 tallies in the frequency table for one time per week. Where there are 4 “x’s” over the answer two on the line plot, there are 4 tallies in the frequency table for two times per week. And so on.

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But what you may not be able to see as clearly in the frequency table is the distribution of this information. As you can see from the line plot, the distribution here is not uniform. In other words, the distribution is unevenly spread over the line. Most of the data is clustered within the lower half of the graph.

Going back to our example, to answer part (a), the answer “3 times per week” has the highest frequency because there are the most “x’s” over the number 3. This means that of those surveyed, exercising three times per week was the most popular answer.

The range, which is what we’re being asked for in Part (b) of the example, goes from zero times per week to 10 times per week. Zero is the least number of times per week a person surveyed exercises and 10 is the greatest number of times per week a person surveyed exercises.

Part (c) of the example asks: Are there any outliers? An outlier is an unusual data value that is plotted far from where most of the data is clustered. In this example, 10 times per week would be considered an outlier since it’s an unusual response. Visually, you can see that it’s plotted far from where most of the other data is plotted.

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