Where is the median read from a cumulative frequency diagram?

At cumulative frequency \frac{n}{2}.

Linear interpolation formula for a quantile?

L+\frac{position-F{below}}{f}\times w

Typical rule for outliers?

Below Q1-1.5\,IQR or above Q3+1.5\,IQR, if stated in the question.

What five numbers define a box plot?

Minimum, Q1, median, Q3, maximum (with outliers shown separately).

What must you compare when comparing two box plots?

An average (median) and a spread (IQR or range), in context.

What does the area of a bar represent if total area is 1?

The probability (relative frequency) of the class.

Single-variable data: diagrams and histogramsEdexcel 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?: $\frac{\text{frequency}}{\text{class width}}$
A bar has frequency density 3.2 and width 5. Frequency?: $3.2\times5=16$ .
Where do you plot a frequency polygon point?: At the midpoint of each class.
Where do you plot cumulative frequency?: At the upper class boundary.
Where is the median read from a cumulative frequency diagram?: At cumulative frequency $\frac{n}{2}$ .
Positions of $Q_1$ and $Q_3$ on a cumulative frequency graph?: $\frac{n}{4}$ and $\frac{3n}{4}$ .
Linear interpolation formula for a quantile?: $L+\frac{\text{position}-F_{\text{below}}}{f}\times w$
Define the interquartile range.: $Q_3-Q_1$ .
Typical rule for outliers?: Below $Q_1-1.5\,\text{IQR}$ or above $Q_3+1.5\,\text{IQR}$ , if stated in the question.
What five numbers define a box plot?: Minimum, $Q_1$ , median, $Q_3$ , maximum (with outliers shown separately).
What must you compare when comparing two box plots?: An average (median) and a spread (IQR or range), in context.
What does the area of a bar represent if total area is 1?: The probability (relative frequency) of the class.

Exam questions on Single-variable data: diagrams and histograms

The durations of phone calls made from an office are shown in a histogram. The bar for calls from 2 to 6 minutes has frequency density 7.5, the bar for calls from 6 to 10 minutes represents 18 calls, and the bar for calls from 10 to 20 minutes has frequency density 1.2.
Estimate the number of calls that lasted between 8 and 12 minutes.2 marks
The marks, out of 50, scored by 11 students in a test were 12, 15, 17, 18, 20, 21, 23, 25, 26, 28 and 45. For this data take the lower quartile to be the median of the lowest five marks and the upper quartile to be the median of the highest five marks. A value is an outlier if it is more than $1.5\times$ IQR above the upper quartile or below the lower quartile.
Show that the mark of 45 is an outlier.2 marks
The heights of 100 plants are summarised as follows: 8 plants are under 10 cm, 30 are under 20 cm, 65 are under 30 cm, 90 are under 40 cm and all 100 are under 60 cm. Assume the heights are spread evenly within each class.
Use linear interpolation to estimate the median height of the plants.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).