Staff at public schools are required to adhere to stipulated percentages or fractions relating to the total number of weekly periods based on their post level - NSC Mathematical Literacy - Question 3 - 2024 - Paper 1

To find the mode from the Moloto PS periods data:

3, 3, 3, 5, 8, 10, 23, 27, 29, 31, 31, 31, 32, 32, 32

The number 31 appears 3 times, and is the most frequent. Hence, the modal number of periods is 31.

Using the stipulation for the deputy principal's teaching hours:

If the deputy principal teaches between 5% and 60% of 40 periods:

Lower Bound:

$D_{min} = 0.05 imes 40 = 2$ Upper Bound:

$D_{max} = 0.6 imes 40 = 24$

Hence, D can be any value between 2 and 24.

The mean for Woodhill SS is 33.

To calculate the median, first arrange the values in ascending order:

2, 3, 3, 3, 5, 6, 6, 8, 8, 10, 23, 27, 29, 30, 31, 31, 31, 32, 32, 32, 36, 36, 37

There are 20 data points, so the median will be the average of the 10th and 11th values:

Median = $\frac{10 + 23}{2} = 16.5$

This shows the median (16.5) is less affected by outliers than the mean (33), making it a better reflection of typical teaching times.

In the data from Moloto PS, the numbers of staff members who teach 29 or more periods include:

29, 31, 31, 31, 32, 32, 32

This gives us a count of 7 instances. There are a total of 15 staff members.

Thus, the probability as a fraction is:

$\text{Probability} = \frac{7}{15}$