2.1 Drawing box plots

Here we will construct a box plot for the following monthly rainfall data for Stornoway in Scotland.

To construct the box plot, we need a reminder of how to calculate some measures of location that we looked at in Week 3. Checking and refreshing prior knowledge before teaching a new topic is an important element of well-designed teaching. For these calculations, it would be helpful to have the rainfall data in numerical order.

Table 2 Rainfall data (mm), ordered for Stornoway during 2023

Note: for consistency, all values have also been written to one decimal place.

• The median:

The median (Q2) of a set of numbers is the middle value when the data is written in order.

Having re-ordered the data set of 12 items from smallest to biggest in Table 2, the median is found halfway between the 6th and 7th data item.

(92.2+106.0)/2=99.1 or 92.2+ 1/2 (106.0-92.2)=99.1

• The quartiles:

The lower quartile (Q¬¬1) is found a quarter of the way between the 3rd and 4th data item.

47.6+ 1/4 (80.2-47.6)=55.75

The upper quartile (Q¬¬3) is found three quarters of the way between the 9th and 10th data item.

127.0+ 3/4 (143.2-127.0)=139.15

• The extremes:

The minimum value is sometimes called the lower extreme. It is the smallest data value in a set. For Stornoway, the minimum rainfall value is 30.4 The maximum value is sometimes called the upper extreme. It is the largest data value in a set. Here, the maximum rainfall value is 196.0

Activity 3

Timing: Allow 10 minutes

Here is the monthly rainfall data from four locations in the UK for 2023

Table 3 Rainfall data

Add table here, source https://www.metoffice.gov.uk/research/climate/maps-and-data/historic-station-data Note to BOC team: Could this data (Table 3) above please be incorporated as an interactive spreadsheet so learners can easily sort each column of data without having to complete this ordering ‘by hand’?

Use this raw data to complete the following table of information about measures of location for at least two other locations given.

Table 4 Summary measures for rainfall data

Add table here hide Hide reveal table to be added here

Table 5 Summary values for the rainfall data (completed)

The five measures calculated in Activity 3 are sometimes called a five-figure summary of the data.

Using this five-figure summary you can create the box plot for the data. Here is the box plot for the Stornoway data:

Figure 4 Box plot of rainfall, Stornoway

image to be added here

I wonder if you can identify how the five-figure summary has been used to create this plot.

Activity 4

Timing: Allow 5 minutes

Label the summary statistic positions on this box plot

Figure 5 Labelled box plot of rainfall, Stornoway

Labels to be chosen from: lower quartile, maximum, median, minimum, upper quartile Note to BOC team: would be nice as a ‘drag and drop’ labelling activity answers - (a) Median (Q2) (b) Minimum or lower extreme (c) Maximum or upper extreme (d) Lower quartile (Q1)

The central feature of this diagram is a box – hence the name box plot. One dimension of the box – horizontal here – follows a labelled axis. The box extends from the lower quartile at the left-hand edge of the box to the upper quartile at the right-hand edge. This part of the diagram contains 50% of the values in the data set. There is no meaning associated with the other dimension of the box.

Box plots are sometimes called box-and-whisker diagrams – can you see why?

In the Stornoway rainfall plot above, the whiskers extend all the way out to the extremes. Each whisker covers 25% of the dataset.