Frequency density formula?

Frequency divided by class width.

Why use frequency density?

Class widths may be unequal, so heights must be adjusted.

How do you find Q1 from n ordered values?

Position \frac n4: if whole, take the mean of that value and the next; otherwise round up.

What is a back-to-back stem and leaf diagram?

Two data sets sharing one stem, with leaves on opposite sides.

What does a box plot show?

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

Two ingredients of comparing distributions?

A comparison of location (median) and of spread (IQR or range), in context.

Histograms, stem and leaf diagrams and box plotsEdexcel International A Level Maths: Flashcards

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What does the area of a bar in a histogram represent?

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What does the area of a bar in a histogram represent?: The frequency.
Frequency density formula?: Frequency divided by class width.
Why use frequency density?: Class widths may be unequal, so heights must be adjusted.
Position of the median for $n$ values?: $\frac{n+1}{2}$ th value.
How do you find $Q_1$ from $n$ ordered values?: Position $\frac n4$ : if whole, take the mean of that value and the next; otherwise round up.
What must every stem and leaf diagram have?: A key; ordered leaves.
What is a back-to-back stem and leaf diagram?: Two data sets sharing one stem, with leaves on opposite sides.
What does a box plot show?: Minimum, lower quartile, median, upper quartile and maximum.
Interquartile range formula?: $Q_3-Q_1$
Condition for positive skew?: $Q_3-Q_2>Q_2-Q_1$
Two ingredients of comparing distributions?: A comparison of location (median) and of spread (IQR or range), in context.
What fraction of data lies between $Q_1$ and $Q_3$ ?: Half (50%).

Exam questions on Histograms, stem and leaf diagrams and box plots

The lengths of 60 phone calls are grouped as follows: 12 calls lasted from 0 to 2 minutes, 21 calls from 2 to 5 minutes, 15 calls from 5 to 10 minutes, and 12 calls from 10 to 20 minutes. A histogram is drawn with frequency density on the vertical axis.
In the histogram, the bar for the class 2 to 5 minutes is 3.5 cm tall. Find the height of the bar for the class 10 to 20 minutes.2 marks
The scores of 15 players in a game are 23, 27, 31, 34, 34, 38, 41, 42, 45, 47, 52, 53, 58, 61 and 66. They are shown in an ordered stem and leaf diagram.
Describe the skewness of the distribution, justifying your answer using the quartiles.2 marks
The times, in seconds, taken by 12 boys and 12 girls to complete an obstacle course are shown in a back-to-back stem and leaf diagram. The boys' times are 41, 43, 45, 47, 48, 52, 54, 55, 58, 61, 63 and 69. The girls' times are 38, 40, 42, 44, 45, 46, 49, 51, 53, 55, 57 and 62.
Find the median and the interquartile range of the girls' times.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).