Higher only · histograms

Histograms.
The area is
the frequency.

not the height

when the groups are different widths —

Density

frequency density = frequencyclass width

that is the height of each bar

step 1 of 4

Frequency density

1. Work out the width of each class.

2. Frequency ÷ width, for every row.

✓ 8 ÷ 10 = 0.8, 12 ÷ 5 = 2.4 …

time (min)	freq	width	f.d.
0 < t ≤ 10	8	10	0.8
10 < t ≤ 15	12	5	2.4
15 < t ≤ 20	15	5	3.0
20 < t ≤ 40	10	20	0.5

step 2 of 4

Draw the bars

1. The vertical axis is frequency density.

2. Each bar spans its class, with no gaps.

✓ Wide class: the people are spread out

step 3 of 4

Read a frequency

1. Frequency = area of the bar.

2. Width 5 × height 3.0 = 15 people.

✓ Area = width × frequency density

step 4 of 4

Part of a bar

1. How many took 20 to 30 minutes?

2. Only that part: width 10 × height 0.5.

✓ 5 people

histograms —

Height

frequency ÷ class width

Area

the frequency

Part of a bar

width of that part × height

No scale given? Use a bar you know
to find what one square is worth.

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