Question Video: Completing a Grouped Frequency Table Mathematics

Complete the frequency table which shows the marks a group of students received in a test.


Video Transcript

Complete the frequency table which shows the marks a group of students received in a test.

We’re given a grouped frequency table containing, in the first row, the possible marks the students could get in the test, split into distinct classes or groups. And in the second row, we have the frequencies, which is the number of students who attained the marks in each of the given classes of marks. So, for example, the frequency for the class representing marks from 35 to 39 is nine. This means that the test marks for nine students were between 35 and 39 inclusive.

We note that apart from the final class representing 50 or more marks, each class has a range of five marks. And we see from the final column that there were a total of 50 students who took the test. We’re asked to complete the table, and we see there’s one empty cell in the row of frequencies. So to complete the table, we need to find the number of students that this cell should contain. That’s the number of students whose test marks ranged from 45 to 49 inclusive.

Now since the total frequency is equal to the number of students who took the test, to find the missing value, we can sum all of the given frequencies and subtract our result from the total of 50. The number of students in all the other classes is four plus five plus 15 plus nine plus 10 plus four, which is 47. And 50 minus 47 equals three. So, we can complete the table with a frequency of three in the class representing marks from 45 to 49.

We can check that we have the correct number of students by summing all of the frequencies now in the table. And we see that, in fact, they do sum to 50, which is the total frequency.

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