In the lesson's histogram, which class has the tallest bar?

Histograms: drawing, reading and estimating

In a histogram the area of each bar is the frequency. That lets you draw one from a table and estimate how many values lie in any range.

GCSE · 1MA1 · S3, S4
International GCSE · 4MA1 · 6.1
About 18 minutes
Higher tier

Practise this lesson free (6 questions)

Drawing

Work out frequency density = frequency ÷ class width for each class, then draw bars with no gaps at those heights.

Time t (min)	Frequency	Class width	Frequency density
0 < t ≤ 10	8	10	0.8
10 < t ≤ 15	15	5	3
15 < t ≤ 20	20	5	4
20 < t ≤ 30	12	10	1.2
30 < t ≤ 50	10	20	0.5

Estimating in part of a class

How many took between 25 and 40 minutes?
25 to 30 is half of the 20 to 30 class: 510 × 12 = 6
30 to 40 is half of the 30 to 50 class: 1020 × 10 = 5
Estimate = 11. This assumes values are spread evenly within each class.

Estimating from a histogram: 6 + 5 = 11 people took 25 to 40 minutes.

Estimating the median

There are 65 values, so the median is about the 32.5th.
Cumulative frequencies: 8, 23, 43, 55, 65. The median is in 15 < t ≤ 20.
It is 9.5 values into a class of 20 values and width 5: 15 + 9.520 × 5 = 17.4 minutes.

Worked example

Use the table in the lesson. Estimate how many people took between 25 and 40 minutes.

From 20 < t ≤ 30: 510 × 12 = 6
From 30 < t ≤ 50: 1020 × 10 = 5

Answer: 11

Key idea

Frequency density = frequency ÷ width; frequency = area. For part of a class, take the same fraction of its frequency. The median is at n/2 through the data.

Key words

Histogram: A chart for grouped continuous data where the area of each bar represents frequency.
Estimate: An approximate answer, usually found by rounding each number to 1 significant figure.
Range: The largest value minus the smallest value. It measures spread.
Frequency density: Frequency ÷ class width. It is the height of each bar in a histogram.
Density: Mass per unit volume: density = mass ÷ volume, for example in g/cm^{3}.
Median: The middle value when the data are in order.

All GCSE and International GCSE Mathematics key terms and definitions →

Quick check

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Extra practice

2 more questions

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A bar for 0 < t ≤ 10 has frequency density 1.2. Find the frequency.
Show the answer
Answer: 12
Width 10. 1.2 × 10 = 12.
A histogram is drawn for this table. Mass m (kg): 0 < m ≤ 10, frequency 6; 10 < m ≤ 30, frequency 24; 30 < m ≤ 40, frequency 15; 40 < m ≤ 60, frequency 10. Which class has the tallest bar?
1. 0 < m ≤ 10
2. 30 < m ≤ 40
3. 40 < m ≤ 60
4. 10 < m ≤ 30
Show the answer
Answer: 30 < m ≤ 40
Frequency densities: 0.6, 1.2, 1.5, 0.5. The tallest bar is 30 < m ≤ 40.

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Practise this lesson free (6 questions)All GCSE and International GCSE Mathematics lessons

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.