Statistics / Unit 1: Data and Displays
1.5 Histograms
Notes
A histogram shows the distribution of a quantitative variable. Values are grouped into equal-width bins, and each bar's height is the number of values in that bin.
- Bars touch because the horizontal axis is a number line. A bar graph has gaps because it shows categories.
- Individual values are not shown, only how many fall in each bin.
- State the rule for values on a boundary. A common rule puts a value on the left endpoint in the higher bin.
- Example: bins 0 to 10, 10 to 20, 20 to 30 with counts 4, 9, 7 describe $4 + 9 + 7 = 20$ values.
Practice
A histogram has bins 0 to 10, 10 to 20, 20 to 30 and 30 to 40 with counts 4, 9, 5 and 2 (a value on a boundary goes in the higher bin). What percent of the values are less than 20?
There are $4 + 9 + 5 + 2 = 20$ values. $\displaystyle \frac{4 + 9}{20} = 0.65$.
The main difference between a bar graph and a histogram is that a histogram:
Histograms bin quantitative data. Bar graphs show categories.
Which statement about histograms is true?
Very wide or very narrow bins can hide or exaggerate features such as peaks.
Ready for more? Take the Unit 1 test.