A histogram represents the distribution of numerical data by grouping values into equal-width, adjacent intervals and showing each interval’s frequency with a bar whose height matches the number of observations it contains. Creating one requires selecting appropriate intervals, placing values consistently at boundaries, and using clear labels and scales; unlike a bar graph, its touching bars indicate continuous numerical intervals rather than separate categories. Unequal-width intervals and frequency-density comparisons are not included.
A histogram shows how numerical data are spread across equal-width intervals.
The numbers of minutes 12 students spent reading are:
Use intervals that are each 5 minutes wide:
These intervals are next to one another and do not overlap. In boundary notation, they mean:
So, a value exactly equal to goes in the – interval.
| Reading time | Values in the interval | Frequency |
|---|---|---|
| – | ||
| – | ||
| – | ||
| – |
The frequency is the number of data values in each interval.
The finished histogram has bars over –, –, –, and –, with heights matching their frequencies. Unlike a bar graph, a histogram’s bars touch.
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