\f{a} (i) Find the summary values for Aida and Brechtis 1J'lrorrlle times._ using Dataplotter or otherwise. Copy and complete the table below. Round values. where necesary+ to one decimal place. The mean, rounded to one decimal! place, is given. for you as a check that you have entered the data. correctly. Table 2 Summary mines of Wo-nite times for Aida and Brecht for the test 20 days to one decimal place. Aida Brecht U H U: HE (D Mean 20.1 (ii) Use the two measures of location to sayr who. on average. oompletes the game more quickly. Explain your reasoning. {iii} Use all three measures of spread to say which person has the greater variability in the time taken to complete the game. Explain your reasoning. [h] (i) Create boxplots for these two data sets (either drawn by hand or as a printout [rorn Dataplotter or another suitable computer package). Include all the relevant iqurmation required for drawing hexplots as set out in Subsection 1.2 of Unit 11. The summary values can be displayed on the hooped? themselves or in a table to the side of the ciao-rt, as they appear in Deteptotter. {ii} Ilse the relevant hoxplot to say whether the data for Brecht's game times are Symmetric or skewed. If the data are skewed. then state whether they are skewed to the left or skewed to the right. What does this tell you about the spread of the data [or Brecht's game times? (iii) Aida tries to summarise what the hoxplot for her game times is saying. Are the following statements true or Ialse'.' In each case justify your answer. (1) (In about a quarter of the days Aida takes less than 19.5 minutes to complete the game. (2) (In about three-quarters of the (lays Aida takes more than 24 minutes to complete the game. [1] 12] [2] [3] [2] [2] [2] (ivl Aida suspects that one of her game times is an outlier. She checks the list and discovers that she has input one game time incorrectlg,r as 49 instead of 9. Comment how using the cerrect time of 9 will affect each of the mean and median [no calculations are necessary}. [1] page 4 of 10 {c} Aida and Brecht manage to solve the W'onile puzzle on all 20 days. They compare the number of guesses it takes to complete the game on each of the 20 days. The summary values ate in the table below. Table 3 Summary values for the number of guesses it takes Aids: and Brecht to complete the game on each of the 20 days. Aida Brecht M in 2 2 Median 4 4 Max I? Mean 3.9 4.2 SD 1.0 1.3 IQ range 1.5 2 Range 4 4 [1} Are these data discrete or continuous? Justify your answer. [1] {ii} Aida creates dntplots. shown in Figure 1._ [or data on the number of guesses. hut forgets to label them. Which dotplot represents the data [or Aide's number of guesses per game? Explain your answer. [2] \f