Question

A company wished to know if the training programme that they developed
for a particular task was effective. 20 employees were timed performing the
task before and after the training. The times were recorded and are given 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 mean number of
minutes that it took to perform the task before training is 27.2 minutes,
and the mean number of minutes it took to perform the task after
training is 23.1 minutes.
Create boxplots for the two datasets, either using Dataplotter or by
hand. Include either a printout of your boxplots or your complete
hand-drawn boxplots with your answer to this question.

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

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

ii) Are the data more spread out for performing the task before
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 data are
symmetrical or skewed. If the data are skewed, then state whether they
are skewed to the left or skewed to the right, explaining your reasoning
briefly.

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

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

Answer 1