The number of days that Grade 8 learners were absent at a certain high school during a year was recorded - NSC Mathematics - Question 2 - 2021 - Paper 2

To find the number of learners absent for less than 15 days, we can sum the number of learners in the first three intervals:

• For 0 ≤ x < 5: 34 learners
• For 5 ≤ x < 10: 45 learners
• For 10 ≤ x < 15: 98 learners

Thus, the total is:

$34 + 45 + 98 = 177$

So, 177 learners were absent for less than 15 days.

To determine the total number of Grade 8 learners, we sum the number of learners across all categories of absence:

• 0 ≤ x < 5: 34 learners
• 5 ≤ x < 10: 45 learners
• 10 ≤ x < 15: 98 learners
• 15 ≤ x < 20: 43 learners
• 20 ≤ x < 25: 7 learners
• 25 ≤ x < 30: 3 learners

Therefore, the total number of learners is:

$34 + 45 + 98 + 43 + 7 + 3 = 230$

Thus, there are 230 Grade 8 learners at the school.

To create a cumulative frequency graph, we need the cumulative frequencies:

• For 0 ≤ x < 5: 34
• For 5 ≤ x < 10: 34 + 45 = 79
• For 10 ≤ x < 15: 79 + 98 = 177
• For 15 ≤ x < 20: 177 + 43 = 220
• For 20 ≤ x < 25: 220 + 7 = 227
• For 25 ≤ x < 30: 227 + 3 = 230

Plot these points on a graph with the number of days absent on the x-axis and cumulative frequency on the y-axis. Connect the points to form the ogive.

The total number of learners is 230, so the median position is at

$\frac{230}{2} = 115$

Locate 115 on the cumulative frequency graph and find the corresponding number of days absent. Reading from the graph, the median number of days is approximately 12 days (values between 12 and 14 are acceptable).