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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
To find the probability, we first identify the total number of players in the team, which is 15. Next, we count how many players scored between 50 and 80 points in the first tournament. From TABLE 1, the qualifying scores are 62 and 56. Thus, 2 players scored within this range. The probability (P) can then be calculated as follows:
. So, the probability is approximately 0.133.
Step 2
Calculate, as a percentage of the total number of team players, the number of players whose points scored decreased from the first to the second tournament.
Answer
First, we check the points scored by each player in both tournaments. From TABLE 1, we observe that players A, B, C, D, E, F, G, and H had decreased scores. This results in 6 players whose scores decreased. The number of players as a percentage is calculated as:
.
Step 3
Use the points scored by the team in the first tournament and determine: (a) Median score
Answer
First, we arrange the scores of the first tournament in ascending order: 27, 28, 30, 32, 34, 37, 38, 41, 42, 43, 44, 46, 56, 62. Since there are 15 players, the median, being the middle value, is in position 8. Thus, the median score is 41.
Step 4
Use the points scored by the team in the first tournament and determine: (b) Modal score
Answer
The modal score is defined as the score that appears most frequently in the dataset. From the arranged scores, we see that there is no repeating score. Therefore, the modal score does not exist or could be considered as non-defined in this context.
Step 5
Step 6
The box and whisker plots below represent the points scored by individual players in the two tournaments. Use the interquartile range and the maximum and minimum values to compare the performance of the team during the two tournaments.
Answer
From the box plots, we compare the interquartile ranges of both tournaments. We find that:
- Tournament 1 IQR: 14
- Tournament 2 IQR: The interquartile range can be calculated based on the boxes in the plot.
Evaluating maximum and minimum values from the plots, we can conclude that Tournament 1 was more consistent while Tournament 2 had a higher maximum score, indicating improved performance from the team overall.