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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
1.1.1 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, first identify the players who scored between 50 and 80 points in the first tournament. The scores are: 66, 62. This gives us 2 players who scored in that range. The total number of players is 12.
The probability is calculated as:
Thus, the probability is approximately 0.167.
Step 2
1.1.2 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
In the first tournament, the players' scores are: 27, 41, 53, 32, 42, 28, 43, 44, 66, 62, 36, 38.
In the second tournament, their scores are: 10, 17, 8, 14, 33, 48, 53, 63, 70, 81, 100.
Now, we can compare the scores:
- Players A, B, D, E, F, G, H have decreased scores.
That's 6 players who scored less in the second tournament.
The percentage of players whose scores decreased is:
So, 50% of the players had decreased points.
Step 3
1.1.3 Use the points scored by the team in the first tournament and determine: (a) Median score
Answer
First, arrange the scores from the first tournament in ascending order:
27, 28, 32, 36, 38, 41, 42, 43, 44, 53, 62, 66.
There are 12 scores. The median is the average of the 6th and 7th scores:
Step 4
1.1.3 Use the points scored by the team in the first tournament and determine: (b) Modal score
Answer
The mode is the score that appears most frequently. In the first tournament scores:
27, 41, 53, 32, 42, 28, 43, 44, 66, 62, 36, 38.
Each score appears only once, making there is no mode in this data set.
Step 5
1.1.3 Use the points scored by the team in the first tournament and determine: (c) Interquartile range (IQR)
Answer
To find the interquartile range, we need to calculate the first quartile (Q1) and the third quartile (Q3).
From the ordered data:
-
Q1 (1st quartile) is the median of the first half (27, 28, 32, 36, 38, 41):
-
Q3 (3rd quartile) is the median of the second half (42, 43, 44, 53, 62, 66):
Now, calculate the IQR:
Step 6
1.1.4 Use the interquartile range and the maximum and minimum values to compare the performance of the team during the two tournaments.
Answer
The interquartile range (IQR) for tournament 1 is found to be 14.5. The maximum score for tournament 1 is 66 and the minimum is 27.
In tournament 2, the IQR can be found similarly, with maximum at 100 and minimum at 10.
Comparatively, the IQR of tournament 1 is smaller than that of tournament 2. This indicates that players had less variability in their scores during the first tournament.
This analysis suggests performance was more consistent in the first tournament.