Histograms: bars for ranges of numbers

0:00We measured 30 plants in centimetres. How can we show their heights on one graph?

0:06First, sort the heights into intervals. An interval is a range of numbers, like 10 to under 15.

0:15The frequency is how many plants fall in each interval: 3, 8, 12 and 7.

0:23Check: 3 plus 8 plus 12 plus 7 is 30, so every plant is counted.

0:31A histogram is a graph of data in intervals. Height goes along the horizontal axis, frequency up the vertical axis.

0:40Every interval is 5 centimetres wide, so each bar's height is its frequency: 3, 8, 12 and 7.

0:51The bars touch, because the intervals run on with no gaps between them.

0:56Sorted by type, the same plants make a bar graph. Bean, pea and tomato are separate categories, so its bars have gaps.

1:06A plant exactly 20 centimetres tall sits on a boundary, where one interval ends and the next begins.

1:14Under 20 means less than 20, so it is not in 15 to under 20. It goes in 20 to under 25.

1:24Counting a boundary value in both intervals is a common mistake. Count it once.

1:31Now, how many plants are 20 centimetres or taller?

1:36Take every bar from 20 upward: 12 plants from 20 to under 25, and 7 from 25 to under 30.

1:4512 plus 7 is 19, so 19 plants are 20 centimetres or taller.

1:52Check: 3 plus 8 is 11 plants under 20, and 30 minus 11 is 19.

2:00A histogram shows how many values fall in each interval, with bars that touch.