The table shows the marks that 30 students received in a mathematics test. How many students received 36 marks or more?
In this question, we are given the marks of 30 students in a test. We are asked to calculate the number of students who scored 36 marks or more.
One way of doing this is using a grouped frequency table. When creating a grouped frequency table, we must ensure that classes are
exhaustive. There should be a class for every data value in the set. The classes should also be mutually exclusive. There should be no overlapping data values between classes. Finally, the classes should be continuous. There should be no gaps between the classes.
In this question, we will use the groups 21 to 25, 26 to 30, 31 to 35, 36 to 40, 41
to 45, and 46 to 50 marks.
Note that we must ensure that 36 is the lower bound of one of the groups to answer
this question. We do this as the lowest mark was 21 and the highest mark was 50. We can see from the table that five students scored between 21 and 25, so the first
frequency is five. Six students received a mark between 26 and 30. Next, we see that the next frequency is nine as this number of students fell in the
range 31 to 35. Three students scored between 36 and 40 marks. There was one student who received 44 marks. And this was the only score between 41 and 45, so the next frequency is one. Finally, six students received a mark in the interval 46 to 50.
At this stage, it is worth checking that our six frequencies sum to 30. Since this is the case, we know that we have counted every student in the grouped
Recalling that we want to calculate the number of students who scored 36 marks or
more, we need to find the sum of the last three frequencies. Three plus one plus six is equal to 10. We can therefore conclude that 10 students received a mark of 36 or more in the