Question Video: Finding the Midpoints of Each Class in a Frequency Distribution | Nagwa Question Video: Finding the Midpoints of Each Class in a Frequency Distribution | Nagwa

# Question Video: Finding the Midpoints of Each Class in a Frequency Distribution Mathematics • Second Year of Preparatory School

## Join Nagwa Classes

Consider the following frequency distribution. Complete the table by finding the midpoints of each class.

02:52

### Video Transcript

Consider the following frequency distribution. Complete the table by finding the midpoints of each class.

This data set has been presented in a grouped frequency distribution. The classes are given as open intervals: zero dash, five dash, ten dash, and so on, up to 25 dash.

To determine the midpoint of each interval, which would be required if we wanted to estimate the mean of the data, we first need to determine the upper boundary for each class. We assume that there are no gaps in the data. So the upper boundary for each class is the lower boundary for the previous one. The upper boundary for the first class is therefore five. We could express this as a double-sided inequality: 𝑥 is greater than or equal to zero and strictly less than five.

Using a weak inequality at the lower end of the class and a strict inequality at the upper end ensures that the classes have no gaps but also don’t overlap. Alternatively, we could add the upper boundary of each class into the table, remembering that when we write, for example, five to 10, we mean greater than or equal to five but strictly less than 10. Then, to calculate the midpoint of each class, we take the mean of the upper and lower boundaries for that class.

For example, we can see that for the two midpoints that are already filled in, 7.5 is equal to five plus 10 over two, and 17.5 is equal to 15 plus 20 over two. The midpoint for the first class is therefore zero plus five over two, which is 2.5. For the third class, it’s 10 plus 15 over two, which is 12.5. And for the fifth class, it’s 20 plus 25 over two, which is 22.5.

There’s one class we haven’t mentioned yet, which is the final one. When determining the upper boundary for this class, we need to assume it has the same width as the previous class. In fact, all classes in this frequency distribution have the same width of five. So, we assume that the upper boundary for the final class is 30, and then the midpoint is calculated as 25 plus 30 over two, which is 27.5.

The four midpoints needed to complete the table are 2.5, 12.5, 22.5, and 27.5.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions