A group of students at a nursing college wrote two tests for the same course - NSC Mathematical Literacy - Question 3 - 2020 - Paper 2

To find the median, we first order the Test 2 scores:

57, 62, 63, 66, 66, 66, 70, 73, 75, 80, 83, 87, 90, 91, 95, 97.

The median is the middle value; since there are 15 scores, the median score is the 8th value, which is 73.

Given that the mean score for Test 1 is calculated using the formula:

$ext{Mean} = \frac{\sum \text{scores}}{n}$

where n is the total number of students (which is 18). If we let Y represent the score of the unknown student, we can set up the equation:

$\frac{90 + 97 + 90 + 88 + 75 + 76 + 79 + Y + 95 + 91 + 61 + 80 + 70 + 70}{15} = 84$

This simplifies to:

$\frac{1030 + Y}{15} = 84$

Multiplying both sides by 15 gives:

$1030 + Y = 1260$

Therefore,

$Y = 1260 - 1030$ $Y = 230$

To identify candidates where the difference between Test 1 and Test 2 scores is 30% or more:

• Oscar: 97% - 57% = 40%
• Tendo: 90% - 63% = 27%
• Esihle: 88% - 66% = 22%
• Kevin: 95% - 97% = -2%

Therefore, only Oscar meets the criteria. Oscar's scores differ by 40%.

To find the interquartile range (IQR), we first calculate the first quartile (Q1) and third quartile (Q3).

Ordering the Test 2 scores: 57, 62, 63, 66, 66, 66, 70, 73, 75, 80, 83, 87, 90, 91, 95, 97.

• Q1 (the 1st quartile) is the median of the first half: 66.
• Q3 (the 3rd quartile) is the median of the second half: 83.

Thus, IQR = Q3 - Q1 = 83 - 66 = 17.

There are 18 candidates in total. Only 6 candidates scored below 85% in Test 2:

• Oscar (57)
• Tendo (63)
• Jim (66)
• Linda (62)
• Cathryn (66)
• Mkhaya (75)

The probability of selecting a candidate who did not get a distinction is:

$P = \frac{6}{18} = \frac{1}{3}$.

By observing the scores of Test 1: 90, 97, 90, 88, 75, 76, 79, 95, 91, 61, 80, 70, 70.

The mode is the value that appears most frequently; here, 90 appears twice, while other scores appear once. Thus, the modal test score for Test 1 is 90.