Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 3, Part B:
Histograms (30 minutes)

In This Part: Constructing a Histogram | Completing the Histogram | Interpreting a Histogram

Like the line plot we explored in Session 2, the stem and leaf plot is a useful device for illustrating variation in data for small data sets (up to about 100 values). For larger data sets, though, the stem and leaf plot is not a practical way to organize data. Instead, you might want to use a histogram. Note 3

Let's start with the stem and leaf plot for a new data set: 52 estimates collected in answer to the question "How long is a minute?":

52 Responses to the Question

 79 67 72 75 64 82 55 56 58 66 60 59 63 75 66 57 72 67 59 61 60 57 61 60 53 30 50 42 39 68 89 67 65 86 39 54 93 52 55 72 56 65 89 33 52 60 70

If the stem and leaf plot is rotated 90° counterclockwise, it looks like this:

To create a histogram for this data, first replace each "leaf" (second digit) with a dot:

While a histogram is similar to a line plot, there are, in fact, differences in the values across the horizontal axis. In a line plot, these numbers represent a single data value. In the plot above, the numbers across the bottom indicate the stems in the original stem and leaf plot. Each number represents an entire interval of values.

For instance, the "3" denotes the stem for all values in the 30s -- that is, the interval (range) of values from 30 up to (but not including) 40. For the purposes of a histogram, it is useful to label this interval "30 to less than 40" (30 to < 40) to remind us that 30 is included but 40 is not.

The "4" denotes the stem for all values in the 40s -- that is, the interval (range) of values from 40 up to (but not including) 50. Again, it is helpful to label this interval "40 to < 50" to remind us that 40 is included but 50 is not.

If we re-label the horizontal axis to show these intervals (groups) of data, the graph below is produced. Again, this graph is similar to a line plot except that the horizontal axis indicates intervals of data values instead of individual data values:

A grouped frequency table can be determined from this display in the following manner:

 • There are four dots over the first group in the interval 30 to < 40. This group has frequency 4. • There is one dot over the second group in the interval 40 to < 50. This group has frequency 1.

If we continue this process for the other groups, we produce the following grouped frequency table:

Interval

Frequency for Interval

 30 to < 40 4 40 to < 50 1 50 to < 60 17 60 to < 70 18 70 to < 80 7 80 to < 90 4 90 to < 100 1

Remember that this table describes ranges of data values rather than specific data values. For instance, we can see that there are seven responses in the interval 70 to < 80, but we have no idea what the actual values are for those responses.

 Session 3: Index | Notes | Solutions | Video