Reading Histograms
Grade 6The key move: area = frequency
Every histogram question that asks you to find a frequency comes down to one thing: area of the bar = frequency. Read off the height (frequency density) and the width (class width), then multiply them together.
The y-axis is always labelled "frequency density", not "frequency". If you see "frequency" on the y-axis, you're looking at a bar chart, not a histogram.
Worked example — reading off frequencies
EXAMPLE
A histogram has a bar for 10 ≤ x < 15 with a height (frequency density) of 4, and a bar for 15 ≤ x < 25 with a height of 2.5. How many data values are in each class?
10 ≤ x < 15: class width = 5. Frequency = 5 × 4 = 20.
15 ≤ x < 25: class width = 10. Frequency = 10 × 2.5 = 25.
10 ≤ x < 15 has 20 values; 15 ≤ x < 25 has 25 values.
Finding what proportion lies in a range
EXAMPLE
Using the same histogram, what fraction of the data lies in the class 10 ≤ x < 15?
Total frequency = 20 + 25 = 45. Class 10 ≤ x < 15 has 20 values. Fraction = 20 ÷ 45 = 4/9. 4/9 of the data lies in the class 10 ≤ x < 15.
Always find all the frequencies first, add them to get the total, then work out the proportion. Trying to work with areas directly is error-prone.
