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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 - NSC Mathematical Literacy - Question 1 - 2017 - Paper 2
Question 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. 1.1.2 Calculate, ... show full transcript
Worked Solution & Example Answer: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 - 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 scored the following points:
- Player A: 27
- Player B: 41
- Player C: 32
- Player D: 42
- Player E: 43
- Player F: 44
- Player G: 46
- Player H: 56
- Player I: 38
- Player J: 44
- Player K: 62
Among these, the scores that fall between 50 and 80 are:
- Player H: 56
- Player I: 62
Thus, there are 2 players who scored between 50 and 80 points.
Total number of players = 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' scores decreased, we compare the scores:
- First Tournament: 27, 41, 32, 42, 43, 44, 46, 56, 38, 44, 62
- Second Tournament: 10, 17, 20, 24, 36, 38, 39, 41, 63, 70, 81, 100
The players whose scores decreased from the first to the second tournament are:
- Player A (27 to 10)
- Player B (41 to 17)
- Player C (32 to 20)
- Player D (42 to 24)
- Player E (43 to 36)
- Player H (56 to 41)
Total decreases = 6 players out of 15.
As a percentage:
Step 3
Use the points scored by the team in the first tournament and determine: (a) Median score
Answer
To find the median, we first list the scores in ascending order:
27, 32, 38, 41, 42, 43, 44, 44, 46, 56, 62
Since there are 11 scores, the median is the middle value, which is the 6th score:
Median = 43.
Step 4
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. From the first tournament scores:
27, 32, 38, 41, 42, 43, 44, 44, 46, 56, 62
Here, the score 44 appears twice, while all others appear once. Thus, the modal score is:
Modal = 44.
Step 5
Use the points scored by the team in the first tournament and determine: (c) Interquartile range (IQR)
Answer
First, we find the quartiles:
To find Q1 (the first quartile) we take the median of the lower half:
Lower half: 27, 32, 38, 41, 42 (Median = 38)
To find Q3 (the third quartile) we take the median of the upper half:
Upper half: 43, 44, 44, 46, 56, 62 (Median = 46)
Now, we calculate the IQR:
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
In the box and whisker plots, we analyze the range of scores:
- First Tournament: IQR = 8, Minimum = 27, Maximum = 62.
- Second Tournament: IQR = 14, Minimum = 10, Maximum = 100.
Here, the IQR of the second tournament is greater, indicating that the spread of scores was wider and potentially more players improved their performance. However, the lower minimum score in the second tournament suggests that while some players improved, others performed significantly worse.