WJEC Maths for AS: Applied sample

2 Data presentation and interpretation 22 The horizontal lines which protrude out from either side of the box extend to the minimum and the maximum values in the set of data as long as none of these values are outliers. These are the whiskers and their ends are marked by two shorter vertical lines. Values higher than Q 3 + 1.5 × IQR or lower than Q 1 − 1.5 × IQR are called outliers and these are plotted to the right of the right whisker or the left of the left whisker. Example 1 Plot a box and whisker diagram using the data below: 1, 5, 1, 2, 4, 3, 3, 2, 1, 5, 4, 5, 1, 6, 2, 0, 6 Answer 1 First order the data 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 Find n which is the number of data values in the list ( n = 17 here) The median is at the n + 1 2 value. In this case n is 17 so 17 + 1 2 = 9th value, which is 3. Median = 3. The lower quartile is at the n + 1 4 value. As n is 17 this is the 4.5th value which is the average of the 4th and 5th values. Lower quartile = 1 The upper quartile is at the n + 1 4 × 3 value. As n is 17 this is the 13.5th value, which is the average of the 13th and 14th values. Upper quartile = 5. The interquartile range (IQR) = upper quartile − lower quartile = 5 − 1 = 4 The highest and lowest values are 6 and 0, respectively, so the range is 6 − 0 = 6 The box and whisker diagram can now be drawn: 0 1 2 3 4 5 6 Lowest value Lower Median Upper quartile quartile Highest value Using a computer to produce box and whisker diagrams There are many different and free software packages that you can use to produce box and whisker diagrams. You usually enter the values as a list separated by commas. You can then tailor such things as headings, scales, etc., before the diagram is produced. The software usually produces a vertical box and whisker