Original Maiths practice · Edexcel IGCSE Maths
Find frequency from histogram density
A histogram bar covers the interval 30 ≤ t < 45 and has frequency density 2.4. Find how many observations the bar represents. This original Maiths question checks the relationship between bar area and frequency.
Step-by-step solution
- Identify the class boundaries rather than reading the height as the answer. The interval runs from 30 to 45, so its width is 45 − 30 = 15.
- Rearrange frequency density = frequency ÷ class width to obtain frequency = frequency density × class width.
- Substitute the given values: frequency = 2.4 × 15 = 36. The count is a whole number even though the density is a decimal.
Check the answer
Reverse the operation: 36 ÷ 15 = 2.4, recovering the stated density. If the horizontal variable is measured in minutes, density has units of observations per minute and multiplying by minutes leaves a count.
Common errors
The answer is not 2.4, because bar height represents density. It is also not 108, which would use 45 as the width rather than subtracting the lower class boundary.
Extend your understanding
Another bar has width 10 and density 3. Its frequency is 30. Although it is taller, it contains fewer observations than the first bar. This comparison is why unequal-width histograms must be interpreted through area.
Skill and difficulty
Skill: Histograms. This is a method-practice question: attempt it after learning the corresponding topic, then use the extension to check deeper understanding. This learning label is not an official examination grade.
Related resources
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