MAED 3103 - 002 SPRING 1996

Introduction to Data Analysis
Using the TI-82 Calculator
Section 3

Organizing Data - Stem and Leaf Plots

We have several ways of displaying and interpreting sets of data. A line plot tends to have a sizable spread that can make it difficult to recognize patterns, and the presentation may be less effective as a tool to aid in the interpretation of the data. The stem-and-leaf plot provides an alternative method and allows us to compare two sets of data. These are easier to construct than histograms and bar graphs, but give us essentially the same type of information.

First, find the smallest value and the largest value. The smallest value for any of the three varieties is 186 and the largest is 266 grams. This means that we are going to use the numbers 18 through 26 as the stems.

Next, write the stems vertically with a line to the right.

18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |

Lastly, separate each data value into a stem and a leaf and put the leaves on the plot to the right of the stem. For example, the first data value from the Red Delicious apples is 204. The stem is 20 and the leaf is 4. The second value has a stem of 21 and a leaf of 2. Continuing in this way we get the following plot for the Red Delicious apples.

18 |
19 |
20 |4
21 |2 5
22 |1 1 2 3 4 5 6 6 7
23 |1 1 3 3 4 7 8 9 9 9
24 |0 1 1 1 2 5 7 8
25 |3 5 7
26 |3 4 6

The numbers in the stems are the hundreds and tens places of each of the data values while the leaves are the numbers in the ones places of the data entries.

The stem plot shows the shape of the data a little more clearly than the line plot. This is because it is somewhat summarized. Here we see a fairly symmetrical bell-shaped distributions with the lows balancing the highs.

Stem plots also offer us the opportunity to directly compare two sets of grouped data. We draw the stem and put the leaves of one set of data on the left and the leaves of the second set of data on the right. These are sometimes called back-to-back stem plots.

Red DeliciousGranny Smith
          | 18 |6          
          | 19 |3          
         4| 20 |56669      
        52| 21 |0124456779 
 766543211| 22 |00134788999
9998743311| 23 |01579      
  87521110| 24 |015        
       753 | 25 |           
       643| 26 |           

We can see that both sets have the same basic shape, but "peak" at different places. Two of the basic aspects that we can describe numerically about a set of data are the center of the distribution and the spread of the distribution. There are two different ways to measure the location and the spread:

Determining the median and the range is much simpler, requiring only counting and understanding the fractions ¼, ½, and ¾. We will work with both.

Section 4: Means, Medians and Outliers

MAED 3103 - Technology and Mathematics Education Spring 1996


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Last updated 2/7/96 by

David Royster david.royster@uky.edu