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Interpret line plots

A line plot represents a numerical data set by placing one mark above each value for every observation, allowing the frequency, least and greatest values, range, clusters, gaps, and possible outliers to be interpreted. At this level, learners compare distributions and use the plot to reason about center and variability, including mean or median when appropriate, while distinguishing the number of marks from the numerical values themselves; formal inference and more advanced statistical displays are not included.

Detailed Explanation: Interpret line plots

A line plot uses one mark for each observation in a data set. The number written on the number line is the value, while the number of marks above it is the frequency, or how many times that value occurs.

Suppose this line plot shows the number of books read by 9 students:

Number of books456789101112
MarksXXXXXXXXX

You can read the plot step by step.

  1. Find the frequency of each value.
    There is:

    • 1 mark at 4
    • 2 marks at 5
    • 3 marks at 6
    • 2 marks at 7
    • 1 mark at 12

    There are 1+2+3+2+1=91+2+3+2+1=9 marks, so there are 9 observations.

  2. Find the least and greatest values.
    The least value is 44, and the greatest value is 1212.

  3. Find the range.
    The range shows the total spread of the data:

range=greatest value−least value=12−4=8\text{range}=\text{greatest value}-\text{least value}=12-4=8

  1. Look for clusters and gaps.
    The values from 55 to 77 form a cluster because many observations are close together.
    There is a gap from 88 to 1111 because there are no marks there.

  2. Look for a possible outlier.
    The value 1212 is separated from the cluster, so it may be a possible high outlier. We say “possible” because a line plot alone does not prove that it is an outlier.

  3. Describe the center if asked.
    The data values in order are

4, 5, 5, 6, 6, 6, 7, 7, 124,\ 5,\ 5,\ 6,\ 6,\ 6,\ 7,\ 7,\ 12

The middle value is 66, so the median is 66. The mean is

4+5+5+6+6+6+7+7+129=589≈6.4\frac{4+5+5+6+6+6+7+7+12}{9} =\frac{58}{9}\approx 6.4

Both measures describe the center, but the median of 66 may better represent a typical student because the value 1212 is far from the main cluster.

When interpreting a line plot, remember: count the marks to find how many observations there are, and read the number line to find the numerical values.

Learn by doing: Interpret line plots

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    Graphing - Line Plot - Read Value

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