Calculating the mean and modal class from grouped data

curriculum-key-fact
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.

Calculating the mean from grouped data

Example

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

Table showing the weights of children in a 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:

Table showing how to multiply the midpoint and frequency of each group, to calculate the mean weight

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:

\[50 \leq m \textless 60\]

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