Box plots – Higher
A box plot shows a visual representation of the The median is the value of the middle item of data when all the data is arranged in order. and The collective term for the lower quartile and upper quartile of a set of data. of a set of Values, typically letters or numbers..
To draw a box plot, the following information is needed:
- minimum value
- The lower quartile (Q1) is one quarter of the way through the data, after the data have been arranged in order of size.
- median
- The upper quartile (Q3) is three quarters of the way through the data, after the data have been arranged in order of size.
- maximum value
Drawing a box plot from a list of numbers
Box plots can be created from a list of numbers by ordering the numbers and finding the median and lower and upper quartiles.
Example
Draw a box plot for these numbers:
9, 10, 10, 12, 13, 14, 17, 18, 19, 21, 21
The numbers are already in order so the minimum and maximum numbers can be easily read off as 9 and 21, and the middle number can be read as 14.
9, 10, 10, 12, 13, 14, 17, 18, 19, 21, 21
To find the lower quartile, there are 11 numbers, so \(\frac{11 + 1}{4}\) = 3rd number. The lower quartile will be the 3rd number and the upper quartile is the 9th number.
9, 10, 10, 12, 13, 14, 17, 18, 19, 21, 21
Drawing these points onto a number line will give the following box plot.
Drawing a box plot from a cumulative frequency graph
Drawing a box plot from a A running total of the frequencies, added up as you go along. graph is straightforward as long as the median and quartiles have been found.
The guideline for median, lower quartile and upper quartile can be used to plot the sections of the box plot. The minimum and maximum values of the box plot are where the cumulative frequency begins and ends.