How do you find the frequency from a bar?

Multiply frequency density by class width.

What is the modal class of a histogram?

The class with the highest frequency density.

How do you estimate the frequency in part of a class?

Assume even spread: density \times width of the part.

What is relative frequency density?

Frequency \div total \div class width.

How do you find a probability from a relative frequency histogram?

Find the area over the required interval.

Why do histogram bars touch?

The data is continuous, so there are no gaps between classes.

What does a long tail to the right mean?

The distribution is positively skewed.

Data presentation and diagramsAQA A-Level Maths: Flashcards

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What does the area of a histogram bar represent?

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What does the area of a histogram bar represent?: The frequency of that class.
Formula for frequency density?: $\frac{\text{frequency}}{\text{class width}}$
How do you find the frequency from a bar?: Multiply frequency density by class width.
What is the modal class of a histogram?: The class with the highest frequency density.
How do you estimate the frequency in part of a class?: Assume even spread: density $\times$ width of the part.
A class 5 to 15 has frequency 40. Its frequency density?: $\frac{40}{10}=4$
What is relative frequency density?: Frequency $\div$ total $\div$ class width.
In a relative frequency histogram, what is the total area?: $1$
How do you find a probability from a relative frequency histogram?: Find the area over the required interval.
Why do histogram bars touch?: The data is continuous, so there are no gaps between classes.
What does a long tail to the right mean?: The distribution is positively skewed.
Where are cumulative frequencies plotted?: At the upper class boundaries.
What should a stem-and-leaf diagram always include?: A key and ordered leaves.

Exam questions on Data presentation and diagrams

A histogram shows the times, in minutes, taken to serve 80 customers. The classes are 0 to 2, 2 to 5, 5 to 10 and 10 to 20 minutes, with frequency densities 10, 8, 4 and 1.6 respectively.
Estimate the number of customers who took longer than 8 minutes to be served.2 marks
A histogram shows the distances, in km, that commuters travel to work. For the class 10 to 15 km the frequency density is 6, for 15 to 25 km it is 3.5, and for 25 to 45 km it is 0.6.
A student says: 'The bar for 10 to 15 km is the tallest of the three, so more commuters travel 10 to 15 km than travel 15 to 25 km.' Is the student correct? Justify your answer.2 marks
The times, in seconds, taken by 100 pupils to complete a puzzle are recorded in classes. The frequencies are 10 for 0 to 20, 30 for 20 to 30, 40 for 30 to 40, 15 for 40 to 60 and 5 for 60 to 100 seconds.
Find the frequency densities for the classes 0 to 20, 40 to 60 and 60 to 100 seconds.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).