In the previous sections, you interpreted the center and the data surrounding the center, and the spread of dot plots, stem-and-leaf plots, histograms, and box plots. In this section, you are going to use the information discussed in previous sections, and interpret the meaning of the graph based on its shape.

The graphs presented in the lesson are below. Observe the commonalities between the graphs by clicking on each graph.

Use the information from the interactive to answer the following questions:

• What do the graphs have in common?

  Interactive popup. Assistance may be required.

  Need a hint?

  Look at the colored curves, and describe the shape that is the same in most of them.
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  Check Your Answer

  At some point, all of the plots except the stem-and-leaf plot have an area where there are more data points. This is shown by the peak in the line. They also have a long line on one side or the other that includes several data points. The stem-and-leaf plot has a circle around points that are the same and that have several points after them.
• The area on the graph where most of the points are located is often called the “peak.” If there are several more data points on one side of the peak than the other, that side is called a “long tail.” For each graph, state if the long tail is on the left or the right side of the peak.

  Interactive popup. Assistance may be required.

  Need a hint?

  Look at the colored curves. There is a curve and a long line before or after the curve. Decide if the long line is before or after the peak.
  Interactive popup. Assistance may be required.

  Check Your Answer

  U.S. President inaugural ages or dot plot: right side
  Ages of Young Millionaires histogram: left side
  Ages of Young Millionaires box plot: left side

The graphs above had long tails either to the right or the left of the peak. These graphs are skewed, which means they have a “long tail” to either the left or the right of the peak.

Click on an outer circle to read a definition and see a graph for each data distribution description.

Use the interactive and graphs above to answer the following questions:

• State the skew of each graph.

  Interactive popup. Assistance may be required.

  Need a hint?

  Look for the peak of the graph. Are there an equal number of data values to the right and left, or are there more data values to the right or to the left of the peak?
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  Check Your Answer

  U.S. President inaugural ages or dot plot: A slight left skew because there are values to the right, far from the median, 54.5.
  Ages of Young Millionaires histogram: Right skewed because there are values far away from the peak which is 16 years of age.
  Ages of Young Millionaires box plot: Right skewed because there are values to the left, far from the peak, 16 years of age.
• Why is the skew of the graph important? Give an example.

  Interactive popup. Assistance may be required.

  Need a hint?

  The skew shows values that are far away from the center or peak. Would these values ever be important?
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  Check Your Answer

  The skew provides information regarding data points that are not close to the center or peak. If the graph represents student assessment scores, the skew would tell the teacher if there are students who don’t understand the material and need extra assistance, or if there are students who know the material and need more challenging opportunities. For example, if the data is right skewed, there are students who need extra help because they may not understand the material as well as the students with average assessment scores. If the data is left skewed, there are students who may desire more challenging opportunities because their assessment scores are higher than student’s assessment scores at the center or peak.

Practice

Click on the correct column header to move the graphs into the column representing their skew.