The table below shows the amount of time (in hours) that learners aged between 12 and 16 spent playing sport during school holidays - NSC Mathematics - Question 1 - 2016 - Paper 2

The modal class is 40 ≤ x < 60 hours, as it has the highest frequency.

According to the cumulative frequency, a total of 172 learners played sport during the school holidays.

Using the ogive, find the 60% mark of the total students, which is 60% of 172. This results in approximately 103.2. From the ogive, the number of learners above this point can be estimated as 148 learners.

To estimate the mean time, use the cumulative frequencies to calculate the midpoint for each class interval, then apply the formula for the mean:

$ext{Mean} = \frac{\sum (f_i \times x_i)}{N}$

Where $f_i$ is the frequency and $x_i$ the midpoints calculated as follows:

• Class 1: (0 + 20)/2 = 10 hours
• Class 2: (20 + 40)/2 = 30 hours
• Class 3: (40 + 60)/2 = 50 hours
• Class 4: (60 + 80)/2 = 70 hours
• Class 5: (80 + 100)/2 = 90 hours
• Class 6: (100 + 120)/2 = 110 hours

Calculating:

$ext{Mean} = \frac{30 \times 10 + 39 \times 30 + 60 \times 50 + 28 \times 70 + 10 \times 90 + 5 \times 110}{172} = \frac{7880}{172} \approx 45.81$

Thus, the estimated mean time spent is approximately 45.81 hours.