A company wished to know if the training programme that theydeveloped
for a particular task was effective. 20 employees were timedperforming the
task before and after the training. The times were recorded and aregiven in
Table 1.

Table 1 Time spent performing
the task (in minutes)

Before training After training
27 24
28 23
22 20
26 24
21 21
31 24
29 24
27 23
29 22
29 25
28 23
28 24
28 25
27 22
29 23
28 22
26 23
30 24
26 23
25 22
(a) Enter these data into two lists in Dataplotter.
To check that you have entered the values correctly, the meannumber of
minutes that it took to perform the task before training is 27.2minutes,
and the mean number of minutes it took to perform the taskafter
training is 23.1 minutes.
Create boxplots for the two datasets, either using Dataplotter orby
hand. Include either a printout of your boxplots or yourcomplete
hand-drawn boxplots with your answer to this question.

(b) A boxplot gives you a visual representation of the averagevalue using
the median, and also tells you how the data are spread out basedon
the size of the box and the lengths of the whiskers

(i) How do the average times compare for performing the taskbefore
training and after training? Use your boxplots from part (a)to
explain your answer.

ii) Are the data more spread out for performing the taskbefore
training or after training? Use your boxplots from part (a)to
explain your answer.

(c) Use the boxplot for before training to say whether the dataare
symmetrical or skewed. If the data are skewed, then state whetherthey
are skewed to the left or skewed to the right, explaining yourreasoning
briefly.

(d) Create a histogram for each of the datasets, using a startvalue of 20
and an interval of 1. Include either a printout of your histogramsor a
sketch drawn by hand with your answer to this question.

If you draw histograms by hand, then you should use squared paperand
the same axis scale for both histograms to make it easy to comparethem.
(e) Comment on one aspect of the time spent performing the taskthat can
be seen more easily on the histograms than on the boxplots