When data is continuous, we cannot have a column per possible value, as there are infinitely many.

Instead, we use a grouped frequency table to break up the data into specific intervals.

If all the intervals have equal size, then the modal class is the interval in which the most values fall.

We can also estimate the mean from grouped data as if it were a discrete frequency table using the mid-interval values, that is the average of the upper and lower bounds of each interval.

Example

Using the dataset [3.1,5.4,5.6,5.9,6.0,6.9], we can fill in the following table:

so the modal class is 5≤x<6.

If we only had this table (and not the actual values), we could estimate the mean using the mid-interval values:

Then