A large company has its headquarters in the city centre and is trying to improve its carbon footprint by encouraging its employees to use public transport to travel to work. The HR manager, Elena, records the average times for 20 volunteer employees who use public transport one week and private transport the following week. These times, in minutes, are given in Table 1. Table 1 Time spent travelling to work (in minutes) Public transport Private transport 23 30 25 32 25 33 25 34 26 33 26 36 29 37 30 34 31 37 31 36 32 39 33 33 33 41 34 44 34 33 36 41 36 40 37 45 42 45 43 44 (a) Elena considers displaying the data as a pair of dotplots. Do you think that this is a good idea for these particular datasets? Give a brief reason for your answer. (b) Elena decides to create a boxplot for each set of transport times, as displayed in Figure 2. @ 20 23 25 2D 32 35 as 41 44 4? Figure 2 With reference to Subsection 1.2 of Unit 11, state three ways in which she could improve the clarity of her presentation of the boxplots. (c) Elena can't remember which boxplot belongs to which set of transport times. State one way in which she could check by looking at the data for each set of times. (d) Elena realises that the top boxplot represents the data for the public transport times and the bottom boxplot represents the data for the private transport times. She tries to interpret what the boxplots are telling her by making the statements below. For each one, state whether you agree or disagree with her interpretation, and explain why you think she is correct or incorrect. (i) 'On average, the travel times of those employees who took public transport to get to work was less than the travel times of those who used private transport to get to work.' (ii) 'There was less variation in the travel times of those employees who took public transport to get to work than in the travel times of those who used private transport to get to work.' (iii) 'More than half of the travel times of those employees who used private transport to get to work were less than the median.1 (e) Use the boxplot for the travel times of those employees who used private transport to get to work 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. Explain your reasoning briey. (f) Elena creates (poorly presented) histograms for each of the two datasets, shown in Figures 3 and 4 below. 26 29 32 35 as 41 I Figure 3 2s 29 32 35 as 41 44 4? 23 23 II? a. Figure 4 [2] [2] [2] 0) Which histogram belongs to the data for the travel times of those employees who used private transport to get to work Figure 3 or Figure 4? Give a reason for your answer. Comment on one aspect of the comparison of data from the two datasets that can be seen more easily on the histograms than on the boxplots. Comment on one aspect of the comparison of data from the two datasets that can be seen more easily on the boxplots than on the histograms. [2] [2] [2]