Frequency Density
Grade 6Why histograms are different to bar charts
In a bar chart, the height of a bar shows the frequency. That works fine when every category is the same width. In a histogram, bars can have different widths (class intervals), so it's the area of the bar — not the height — that represents frequency.
If you used height directly, a wider bar would look more important than a narrower one with the same frequency. That would mislead you. So we use frequency density on the y-axis instead.
Frequency density = frequency ÷ class width
Worked example — drawing a histogram
EXAMPLE
Times taken (minutes) for 60 runners: 20 ≤ t < 30 (freq 12), 30 ≤ t < 40 (freq 18), 40 ≤ t < 60 (freq 24), 60 ≤ t < 80 (freq 6). Find the frequency density for each group.
20 ≤ t < 30: class width 10, fd = 12 ÷ 10 = 1.2
30 ≤ t < 40: class width 10, fd = 18 ÷ 10 = 1.8
40 ≤ t < 60: class width 20, fd = 24 ÷ 20 = 1.2
60 ≤ t < 80: class width 20, fd = 6 ÷ 20 = 0.3
Plot these values as bar heights. Frequency densities: 1.2, 1.8, 1.2, 0.3
Finding frequency from a histogram
Reverse the formula: Frequency = frequency density × class width
This is the area of the bar. So when you're reading a histogram, identify the height and width of each bar, multiply, and you get the frequency for that class.
Before you start any histogram question, write the formula at the top: fd = f ÷ cw. It keeps you from mixing up which way round to divide.
