To construct a histogram you first construct equally-spaced ranges for the data values, count how many observations fall into each range and then plot the result as a bar chart. Suppose we have the following data:
|
6 |
15 |
7 |
8 |
|
4 |
4 |
2 |
5 |
|
9 |
14 |
8 |
16 |
|
13 |
5 |
20 |
5 |
|
8 |
13 |
8 |
20 |
We can sort the data to make it is easier to develop data ranges:
|
2 |
5 |
8 |
14 |
|
4 |
6 |
8 |
15 |
|
4 |
7 |
9 |
16 |
|
5 |
8 |
13 |
20 |
|
5 |
8 |
13 |
20 |
Since our data is integer valued, it is easy to construct data ranges that are equal, don't overlap and span the data set:
| Range | Start | End | # of obs. |
| 1 | 1 | 5 | 6 |
| 2 | 6 | 10 | 7 |
| 3 | 11 | 15 | 4 |
| 4 | 16 | 20 | 3 |
With the data ranges constructed and the number of observations in each range counted, we can construct the histogram:
While we have a fairly small sample size, this histogram suggests that we would expect more data points to fall in the range 1 - 10 and less in the range 11 - 20. Histograms are useful to graphically show how the sample data varies, which gives us an idea how the data in the population varies.
Return to Normal Distribution Review