Mean for Grouped Data
You already know how to calculate the mean for individual data, right? Just sum up all the values and divide by the number of data points.
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You already know how to calculate the mean for individual data, right? Just sum up all the values and divide by the number of data points.
But what if the data is presented in groups or intervals, like in a frequency distribution table? For example, test scores grouped into , , and .
When data is grouped, we don't know the exact value of each data point within that group. For instance, if there are students in the group, we don't know if their scores are exactly , , , or some other value within that range.
Since we don't know the exact values, we use an assumption or approximation. We assume that all data points within a group are represented by the midpoint of that group (class interval).
The class midpoint (often symbolized as ) is calculated as:
Once we have the midpoint for each class, we can calculate the mean of the grouped data using the formula:
Where:
Consider the grouped data for shoe sales at Store A:
| Shoe Size (Class Interval) | Frequency () |
|---|---|
| Total |
Steps to calculate the Mean:
Find the Midpoint () for each class:
Multiply Frequency by Midpoint () for each class:
Sum all the products ():
Sum all frequencies ():
Calculate the Mean ():
Therefore, the average shoe size sold at Store A is .
Remember, this result is an estimate of the mean because we use midpoints to represent the data within each group. However, this is the standard and most common way to calculate the mean for grouped data.