What is the modal class?

The class with the greatest frequency (when class widths are equal).

What is shown on a frequency histogram?

Class intervals on the horizontal axis; bars touch; heights show frequency (equal class widths).

What is cumulative frequency?

A running total of the frequencies up to and including each class.

At which x-value is each cumulative frequency plotted?

At the upper boundary of its class.

Where do you read the median, Q1 and Q3 on a cumulative frequency graph?

At \frac12n, \frac14n and \frac34n on the cumulative frequency axis.

How do you find the 90th percentile?

Read the value at cumulative frequency \frac{90}{100}n.

What five values are needed for a box and whisker diagram?

Minimum, lower quartile, median, upper quartile, maximum.

How are outliers shown on a box and whisker diagram?

As crosses; the whiskers stop at the most extreme values that are not outliers.

How do you compare two box plots?

Compare the medians (centre) and the IQRs or ranges (spread), in context, with numbers.

Which features suggest data may be normally distributed?

A symmetrical box plot: median in the middle of the box and whiskers of similar length.

4.2 Presenting dataIB Maths: Applications and Interpretation HL: Flashcards

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How are class intervals written for continuous data?

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How are class intervals written for continuous data?: As inequalities without gaps, e.g. $10\le x<20$ , $20\le x<30$ .
What is the modal class?: The class with the greatest frequency (when class widths are equal).
What is shown on a frequency histogram?: Class intervals on the horizontal axis; bars touch; heights show frequency (equal class widths).
What is cumulative frequency?: A running total of the frequencies up to and including each class.
At which x-value is each cumulative frequency plotted?: At the upper boundary of its class.
Where do you read the median, $Q_1$ and $Q_3$ on a cumulative frequency graph?: At $\frac12n$ , $\frac14n$ and $\frac34n$ on the cumulative frequency axis.
How do you find the 90th percentile?: Read the value at cumulative frequency $\frac{90}{100}n$ .
Formulae for IQR and range?: $\text{IQR}=Q_3-Q_1$ ; $\text{range}=\text{max}-\text{min}$ .
What five values are needed for a box and whisker diagram?: Minimum, lower quartile, median, upper quartile, maximum.
How are outliers shown on a box and whisker diagram?: As crosses; the whiskers stop at the most extreme values that are not outliers.
How do you compare two box plots?: Compare the medians (centre) and the IQRs or ranges (spread), in context, with numbers.
Which features suggest data may be normally distributed?: A symmetrical box plot: median in the middle of the box and whiskers of similar length.

Exam questions on 4.2 Presenting data

The masses, $m$ kg, of 50 parcels at a depot are recorded. $0<m\le2$ : 4 parcels; $2<m\le4$ : 11 parcels; $4<m\le6$ : 17 parcels; $6<m\le8$ : 12 parcels; $8<m\le10$ : 6 parcels.
Find the percentage of parcels with a mass greater than 8 kg.2 marks
The heights of 100 plants in a greenhouse are summarised by cumulative frequency. 8 plants have height at most 10 cm, 30 plants at most 20 cm, 68 plants at most 30 cm, 92 plants at most 40 cm and all 100 plants at most 50 cm. Assume that the cumulative frequency rises uniformly (in a straight line) between these heights.
Estimate the number of plants with height between 15 cm and 35 cm.2 marks
Two cafés record the number of customers each day. Café A: minimum 35, lower quartile 48, median 60, upper quartile 72, maximum 91. Café B: minimum 30, lower quartile 50, median 58, upper quartile 66, maximum 110.
Find the interquartile range (IQR) and the range of each café.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).