# Question Video: Completing a Grouped Frequency Table given a Frequency Table Mathematics

The table shows the number of classes of varying sizes in a school. Using the data, complete the frequency table.

02:48

### Video Transcript

The table shows the number of classes of varying sizes in a school. Using the data, complete the frequency table.

We’re given a table where the first row is the number of students in a class. The possible values — that is, the possible number of students in a class — are 16, 17, 18, 19, 20, and 21. The second row in this table is the number of classes in the school with that number of students. So, for example, there were four classes with 16 students, two classes with 17 students, three classes with 18 students, and so on.

It can be helpful when we have a set of data to organize it into groups, which we then put into a group frequency table. To do this, we first define distinct nonoverlapping groups of all the possible values. In this case, the values are the possible class sizes. And in our frequency table, these are collected into three groups, covering class sizes of 16 and 17 students, then 18 and 19, and finally 20 to 21 students.

Now the frequency of a value is defined as the number of times that value occurs in a data set. And in a group frequency table, for each group, the frequency is the sum of the frequencies of each possible value in that group. So for our first group — that is, class sizes of 16 and 17 students — we see from the first table that there were four classes in the school with 16 students and two classes with 17 students. So the frequency for the group class size 16 to 17 in our frequency table is four plus two, which is six. And we can put this into our frequency table as shown.

Next, for our group with class sizes 18 to 19 students, we sum the number of classes with these two class sizes. And that’s three plus five, which is eight. And we can fill in the frequency for the group with class sizes 18 to 19.

Finally, for the group representing class sizes of 20 and 21 students, we have one class with 20 students and four classes with 21 students. And summing these, we have one plus four, which is five. And so this is the frequency for the group representing class sizes of 20 and 21 students.

Hence, the missing frequencies from the frequency table are six, eight, and five. It’s always a good idea to check we have matching totals for our two tables. And we can do this by comparing the sum of the number of classes in the first table, which is 19, with the sum of the frequencies in the second table. This is also equal to 19, so our totals for the number of classes altogether match.