WJEC Maths for AS: Applied sample

23 2.1 Interpreting diagrams for single variable data diagram and most of the packages will list the important measures such as lower quartile, range, median, etc., to save you having to read them off the diagram. A box and whisker diagram is drawn using computer software based on the following set of data 1, 1.2, 1.5, 1.6, 1.9, 2.0, 2.1, 3.4, 4.5, 6.0, 9.2 10 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 × Look carefully at the diagram to check that you can obtain the following quantities from the diagram: Median = 2 Lower quartile = 1.5 Upper quartile = 4.5 Interquartile range = upper quartile − lower quartile = 4.5 − 1.5 = 3 Smallest value = 1 Largest value = 6 Range = largest value − smallest value = 6 − 1 = 5 Outlier = 9.2 Use the Internet to ϐind a free software package that can draw a box and whisker diagram. Check that the software package is able to identify outliers and show them on the diagram. Use the software package to produce a box and whisker diagram which shows the number of emails received per day over a two-week period. 12, 21, 32, 14, 56, 45, 11, 36, 10, 17, 76, 47, 50, 110 Produce a printout of the diagram. Cumulative frequency diagrams If you have a grouped frequency distribution and you are asked to ϐind the median or the quartiles, then you can draw a cumulative frequency diagram and use that. Notice there is a point at 9.2 that is outside the main diagram. This point has been identiϐied as an unrepresentative value called an outlier and it is not included in the data used to plot the box plot. Luckily the software works out outliers and shows them as separate points on the diagram. The outliers are ignored when drawing the rest of the box and whisker diagram. Notice the largest value in this set of data is now 6 as the outlier at 9.2 has been ignored. Active Learning