Box and Whisker Plots

This data shows the scores achieved by fifteen students who took a short maths test. The test was marked out of ten. To construct a box and whisker plot, we need five pieces of information. The median The highest value The lowest value The upper quartile The lower quartile

To find the median and the upper and lower quartiles, we first of all need to arrange the data…. in rank order

0

01

012

0122

01223

012233

The median value is the value where n is the number of data items, so here, n = 15. The median value is the8 th value which is 4

The median value is the value where n is the number of data items, so here, n = 15. The median value is the8 th value which is 4 median

The lower quartile is the value where n is the number of data items, so here, n = 15. The lower quartile is the4 th value which is 2 median

The lower quartile is the value where n is the number of data items, so here, n = 15. The lower quartile is the4 th value which is 2 medianl.q.

The upper quartile is the value where n is the number of data items, so here, n = 15. The upper quartile is the12 th value which is 6 medianl.q.

The upper quartile is the value where n is the number of data items, so here, n = 15. The upper quartile is the12 th value which is 6 medianl.q.

The upper quartile is the value where n is the number of data items, so here, n = 15. The upper quartile is the12 th value which is 6 medianl.q.u.q.

medianl.q.u.q. The lowest value is 0

medianl.q.u.q. The lowest value is 0 The highest value is 9

medianl.q.u.q. The lowest value is 0 The highest value is 9

Now that we have found the median, both quartiles and the highest and lowest values, we have all the information which we need in order to be able to construct the box and whisker diagram

We first of all need some sort of grid. We can use graph paper for this or just ordinary squared paper will do equally well

medianl.q.u.q. First of all we draw the box Data For this, we will need to provide a scale which should be clearly labelled

medianl.q.u.q Data Scores out of ten

medianl.q.u.q. Next we draw the whiskers Data Scores out of ten

Data Scores out of ten

The Box and Whisker Plot is complete Data Scores out of ten

And the final diagram looks like this Data Scores out of ten

Scores out of ten

Box and Whisker plots are useful when comparing sets of data For instance, the scores of the original group of students, group A are now being compared with those of a second group B

Group A Group B Box and Whisker plots are useful when comparing sets of data For instance, the scores of the original group of students, group A are now being compared with those of a second group B Scores out of ten

Group A Group B Scores out of ten By simply examining the two side by side box and whisker plots, we can easily deduce lots of useful information. For instance………

Group A Group B The highest score was in group B Scores out of ten

Group A Group B The lowest score was in group A Scores out of ten

Group A Group B On average, group A did better Scores out of ten

Group A Group B The top 50% of students in group A did better than the bottom 75% of students in group B Scores out of ten

Group A Group B In group A, the middle 50% of the students scores were between 2 and 6 inclusive whereas with group B, the middle 50% of the students scores were contained in a narrower range of values between 2 and 4 inclusive Scores out of ten

Group A Group B We could say a great deal more about these two diagrams Scores out of ten But now it’s your turn to draw and interpret some Box and Whisker diagrams of your own