Wordle is an online game in which players guess the word of the day in six...

  

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Wordle is an online game in which players guess the word of the day in six attempts or fewer. Aida and Brecht record the time and the number of guesses it takes them to complete the game each day to see who is faster. The times (to the nearest minute) that each has taken to complete the game for the previous 20 days are in Table 1. Table 1 Wordle times for Aida and Brecht for the previous 20 days to the nearest minute Aida Brecht 10 21 25 21 16 10 222222222 9 13 14 11 20 9 7 11 29 7 21 8 19 13 15 10 18 8 9 12 23 10 24 8 20 13 12 7 14 6 25 10 15 (a) (i) Is time discrete or continuous? (ii) Find the summary values for Aida and Brecht's Wordle times, using Dataplotter or otherwise. Copy and complete Table 2 below. Round values, where necessary, 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 values of Wordle times for Aida and Brecht for the pre- vious 20 days to one decimal place Min Median Aida Brecht Max Mean 18.2 9.9 SD IQR Range [1] 2 (iii) Use the two measures of location to say who, on average, completes the game more quickly. Explain your reasoning. 2 (iv) 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. [2] (b) (i) Create boxplots for these two data sets (either drawn by hand or using Dataplotter, or a suitable computer package), and include them with the rest of your EMA. The summary values can be displayed on the boxplots themselves or in a table to the side of the chart, as they appear in Dataplotter, (ii) Use the relevant boxplot to say whether the data for Aida'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 for Aida's game times? (ii) Aida tries to summarise what the boxplot for her game times saying. Are the following statements true or false? In each case justify your answer. 13 2 (1) On about a quarter of the days Aida takes less than 14.5 minutes to complete the game. 2 (2) On about three-quarters of the days Aida takes more than 19.5 minutes to complete the game. 12 (c) Aida and Brecht manage to solve the Wordle 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 are in Table 3 below. Table 3 Summary values for the number of guesses it takes Aida and Brecht to complete the game on each of the 20 days Aida Brecht Min 2 3 Median 3 4.5 Max 5 6 Mean 3.5 4.6 SD 0.9 1.2 IQ range 1.0 2.5 Range 3 3 Aida creates dotplots, shown in Figure 1, for data on the number of guesses, but forgets to label them. Which dotplot represents the data for the Aida's number of guesses per game? Explain your answer. Number of Guesses Mumber of Gues Figure 1 Aida's dotplots Wordle is an online game in which players guess the word of the day in six attempts or fewer. Aida and Brecht record the time and the number of guesses it takes them to complete the game each day to see who is faster. The times (to the nearest minute) that each has taken to complete the game for the previous 20 days are in Table 1. Table 1 Wordle times for Aida and Brecht for the previous 20 days to the nearest minute Aida Brecht 10 21 25 21 16 10 222222222 9 13 14 11 20 9 7 11 29 7 21 8 19 13 15 10 18 8 9 12 23 10 24 8 20 13 12 7 14 6 25 10 15 (a) (i) Is time discrete or continuous? (ii) Find the summary values for Aida and Brecht's Wordle times, using Dataplotter or otherwise. Copy and complete Table 2 below. Round values, where necessary, 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 values of Wordle times for Aida and Brecht for the pre- vious 20 days to one decimal place Min Median Aida Brecht Max Mean 18.2 9.9 SD IQR Range [1] 2 (iii) Use the two measures of location to say who, on average, completes the game more quickly. Explain your reasoning. 2 (iv) 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. [2] (b) (i) Create boxplots for these two data sets (either drawn by hand or using Dataplotter, or a suitable computer package), and include them with the rest of your EMA. The summary values can be displayed on the boxplots themselves or in a table to the side of the chart, as they appear in Dataplotter, (ii) Use the relevant boxplot to say whether the data for Aida'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 for Aida's game times? (ii) Aida tries to summarise what the boxplot for her game times saying. Are the following statements true or false? In each case justify your answer. 13 2 (1) On about a quarter of the days Aida takes less than 14.5 minutes to complete the game. 2 (2) On about three-quarters of the days Aida takes more than 19.5 minutes to complete the game. 12 (c) Aida and Brecht manage to solve the Wordle 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 are in Table 3 below. Table 3 Summary values for the number of guesses it takes Aida and Brecht to complete the game on each of the 20 days Aida Brecht Min 2 3 Median 3 4.5 Max 5 6 Mean 3.5 4.6 SD 0.9 1.2 IQ range 1.0 2.5 Range 3 3 Aida creates dotplots, shown in Figure 1, for data on the number of guesses, but forgets to label them. Which dotplot represents the data for the Aida's number of guesses per game? Explain your answer. Number of Guesses Mumber of Gues Figure 1 Aida's dotplots