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Math Lesson 3: Displaying Data Graphically - page 6 / 11

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back-to-back

2. Both a dot plot and a histogram show the shape, center and spread for the distribution of the data, but neither of these graphical representations preserve the actual data values. The stem-and-leaf plot also shows the shape, center and spread of the data, but it has the additional advantage of also displaying the actual data values.

3. Suppose that Mrs. Short wanted to see how her students fared in comparison with Mr. Sneed’s students on the midterm exam. Her students’ scores were as follows: 98, 65, 77, 73, 70, 81, 89, 84, 64, 68, 95, 56, 81 Now add to your stem-and-leaf plot above, by putting the “leaves” for Mrs. Short’s students’ scores to the left of the stems shown in the vertical line. This is called a back-to-back stem-and-leaf plot. Note the order of the leaves on the left. In each stemplot, the leaves increase as they go away from the stems. With such a plot it is easy to compare two data sets by looking at shapes, centers and spreads. Can you tell by looking at the stemplot which class did better?

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Practice problems:

  • 3.

    Mrs. Poppington’s class made the stem- and-leaf plot shown at right after they collected cans for a food drive. Use it to complete the parts below.

    • a.

      List the number of cans collected by each of the students who collected 40 or more. [47, 49, 49, 53, 57]

b. Find the mode of the data. [35]

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1 14

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5 55

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7 99

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Cans collected by Mrs. Poppington’s class

Key 2|3 means 23

  • c.

    Find the median number of cans brought in by the students in Mrs. Poppington’s class. [31]

  • d.

    What do you think the key in the box above is telling you about the stems and leaves? [How to read the stem and leaf plot, that is, the left side of the line is the tens place and the right side is the ones place.]

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