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Basketball is a team sport in which any member of the team can score points in a match - NSC Mathematical Literacy - Question 1 - 2017 - Paper 2
Question 1
Basketball is a team sport in which any member of the team can score points in a match. In TABLE 1 below the manager of a basketball team recorded the number of poin... show full transcript
Worked Solution & Example Answer:Basketball is a team sport in which any member of the team can score points in a match - NSC Mathematical Literacy - Question 1 - 2017 - Paper 2
Step 1
Express the probability (as a decimal) of randomly selecting a member of the team who scored between 50 and 80 points in the first tournament.
Answer
In the first tournament, the players who scored between 50 and 80 points are:
- Player K: 66
- Player L: 62
- Player N: 56
- Player G: 53 Thus, there are 4 players who fit this criterion. The total number of players is 15. Therefore, the probability is:
Step 2
Calculate, as a percentage of the total number of team players, the number of players whose points decreased from the first to the second tournament.
Answer
To determine how many players' points decreased, we compare scores from the first and second tournaments:
- Player A: 10 (decrease)
- Player B: 17 (decrease)
- Player C: 31 (decrease)
- Player D: 28 (decrease)
- Player E: 42 (remains the same)
- Player F: 26 (decrease)
- Player G: 47 (decrease)
- Player H: 33 (decrease)
- Player I: 63 (decrease)
- Player J: 79 (decrease)
- Player K: 81 (decrease)
- Player L: 100 (decrease)
- Player M: 38 (decrease)
- Player N: 44 (decrease)
Out of 15 players, 11 experienced a decrease. Thus, as a percentage, it is:
Step 3
Use the points scored by the team in the first tournament and determine: (a) Median score
Answer
To find the median score, first arrange the scores in ascending order: 27, 28, 30, 32, 38, 41, 42, 43, 44, 53, 56, 62, 66, 30, 38. There are 15 scores, so the median is the 8th score:
The median score is 43.
Step 4
Step 5
Use the points scored by the team in the first tournament and determine: (c) Interquartile range (IQR)
Answer
To find the IQR, first determine Q1 and Q3: Arranging the scores: 27, 28, 30, 32, 38, 41, 42, 43, 44, 53, 56, 62, 66.
Q1 is the median of the first half (27, 28, 30, 32, 38, 41) which is 38. Q3 is the median of the second half (42, 43, 44, 53, 56, 62, 66) which is 56.
Using the formula:
Step 6
Use the interquartile range and the maximum and minimum values to compare the performance of the team during the two tournaments.
Answer
The first tournament had an interquartile range of 18, while the second tournament's data revealed a smaller range, indicating improved player performance. The maximum and minimum scores also saw a shift from the first to second tournament. In terms of team overall performance, the IQR and ranges suggest a more consistent performance in the second tournament.