Calculating the mean and modal class for grouped data is very similar to finding the mean from an ungrouped frequency table, although you do not have all the information about the data within the groups so you can only estimate the mean.

- Question
The following table shows the weights of children in a class.

Using this information:

a) Estimate the mean weight

b) Find the modal class

To estimate the mean weight, you know that \({7}\) children are between \({30~kg}\) and \({40~kg}\). As you do not know exactly how much they weigh, assume that they all weigh \({35~kg}\) (the midpoint of the group).

Find the mean for all the other groups:

a) Estimation of mean = \({1,215}\div{25} = {48.6}~{kg}\)

b) The modal class is the class that has the highest frequency. In this case the modal class is:

\[50 \leq m \textless 60\]