Find the mean for the following frequency distribution:

This is a grouped frequency distribution.

We can find the mean of the data using any of the methods. Since here we have small values of classes, we can find the mean using direct method easily.

We need to create a table using the values, representing class, midpoints, frequency and product of midpoints and frequencies.

Also, this is an inclusive type of data, which needs to be converted into exclusive type of data.

For conversion, we need to subtract 0.5 from the lower class of each interval and add 0.5 to upper class of each interval.

So now, we have

∑x_if_i = 3735 and ∑f_i = 200

Mean is given by

⇒ [Using values from the table]

⇒ Mean = 18.675

Thus, mean is 18.675.