The marks obtained by learners of a certain school in a Mathematics test is represented in the histogram below: Marks for Mathematics Test Marks obtained | Number of learners -----------------|------------------- 0-9 | 0 10-19 | 2 20-29 | 8 30-39 | 12 40-49 | 32 50-59 | 46 60-69 | 22 70-79 | 16 80-89 | 6 90-99 | 0 100 | 0 2.1 How many learners wrote the test? 2.2 Write down the modal class - NSC Mathematics - Question 2 - 2017 - Paper 2

The modal class is the class interval with the highest frequency. From the histogram, the highest frequency is 46, which corresponds to the class interval 50-59.

Therefore, the modal class is 50-59.

To draw the ogive, follow these steps:

1. Calculate the cumulative frequency for each class interval:

   • 0-9: 0
   • 10-19: 2
   • 20-29: 10
   • 30-39: 22
   • 40-49: 54
   • 50-59: 100
   • 60-69: 122
   • 70-79: 138
   • 80-89: 144
   • 90-99: 144
   • 100: 144

2. Plot these cumulative frequencies on a graph against the upper limit of each class interval.

3. Connect the points to draw the ogive.

To estimate the interquartile range (IQR) using the ogive:

1. Find the 1st quartile (Q1) and 3rd quartile (Q3) from the ogive.

2. From the graph, it is noted that:

   • Q1 corresponds to the cumulative frequency at 35, which is approximately 72.
   • Q3 corresponds to the cumulative frequency at 105, which is approximately 89.

3. Calculate the IQR using the formula: $IQR = Q3 - Q1 = 89 - 72 = 17$

Thus, the interquartile range is 17.