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A group of students at a nursing college wrote two tests for the same course - NSC Mathematical Literacy - Question 3 - 2020 - Paper 2
Question 3
A group of students at a nursing college wrote two tests for the same course. TABLE 4 shows the test scores, as percentages, of the students. TABLE 4: TEST RESULTS... show full transcript
Worked Solution & Example Answer:A group of students at a nursing college wrote two tests for the same course - NSC Mathematical Literacy - Question 3 - 2020 - Paper 2
Step 1
Explain, giving a reason, whether the above data is discrete or continuous.
Answer
The given data is discrete. Discrete data is countable and consists of distinct values, while continuous data can take any value within a range. In this scenario, the test scores are represented as whole numbers (percentages) and cannot have fractional values, confirming the data's discrete nature.
Step 2
Determine the median score for Test 2.
Answer
To find the median score for Test 2, first arrange the scores in ascending order: 50, 52, 61, 63, 66, 66, 67, 71, 75, 78, 78. Since there are 11 scores (an odd number), the median is the middle value. Therefore, the median score is the 6th value, which is 66.
Step 3
The mean score for Test 1 was 84%. Calculate the value of Y.
Answer
Let Y be the unknown value. The mean for Test 1 is calculated as follows:
ext{Mean} = rac{ ext{Total scores}}{n} = rac{90 + 87 + 93 + 85 + 70 + 53 + 100 + 66 + 95 + 92 + Y}{11} = 84
Calculating the total of the known scores:
Setting up the equation:
rac{951 + Y}{11} = 84
Multiplying by 11:
Solving for Y:
Since Y represents a score, we cannot accept this result; hence, check the conditions or scores provided again.
Step 4
Identify the candidates whose test scores in both tests differ by 30%.
Answer
To identify candidates whose scores differ by 30%, we can look for those whose Test 1 score minus Test 2 score equals 30, or vice versa. For example:
- Paul: 90 - 50 = 40,
- Oscar: 87 - 52 = 35,
- Tilda: 93 - 61 = 32,
- Fiona: 85 - 63 = 22,
- Jim: 70 - 66 = 4, ... and so forth. The candidates with a 30% difference are Paul and Oscar (40% difference), Tilda and Jim based on the conditions set.
Step 5
Calculate the value of the interquartile range for Test 2.
Answer
The interquartile range (IQR) is calculated as follows:
- Arrange the sorted Test 2 scores: 50, 52, 61, 63, 66, 66, 67, 71, 75, 78, 78.
- Calculate Q1 and Q3:
- Q1 (25th percentile) is the median of the first half: 61
- Q3 (75th percentile) is the median of the second half: 75
- Calculate IQR:
Step 6
Express, in simplified fractional form, the probability of randomly selecting a candidate who did not get a distinction for Test 2.
Answer
To find the probability of selecting a candidate who did not get a distinction (scores below 85):
- Count the candidates who did not score 85 or above in Test 2: 10 candidates (50, 52, 61, 63, 66, 66, 67, 75, 78, 78).
- Total candidates = 11.
- Probability = Number of non-distinction candidates / Total candidates = .
Step 7
Determine the modal test score for Test 1.
Answer
The modal test score is the score that occurs most frequently in the data. For Test 1, the data is: 90, 87, 93, 85, 70, 53, 100, 66, 95, 92. All values are unique; thus the modal test score is not applicable; we may state it 'no mode' as every score is distinct.