Mean of Grouped Data The mean of a grouped data set is a specific measure of central tendency that gives us the "average" value of each group. It can be...
The mean of a grouped data set is a specific measure of central tendency that gives us the "average" value of each group. It can be found by adding up all the values in each group and then dividing the sum by the number of values in the group.
Example:
Suppose we have the following grouped data on the ages of students in different grades:
| Grade | Number of Students | Age |
|---|---|---|
| 4th | 25 | 8 |
| 5th | 30 | 9 |
| 6th | 18 | 10 |
Mean Age:
(8 + 9 + 10) / 3 = 9
Therefore, the mean age of the students in the 4th, 5th, and 6th grades is 9.
Key Points:
The mean is a weighted average, meaning that it gives more weight to groups with more data points.
It is a robust measure of central tendency, meaning that it is relatively insensitive to outliers.
The mean can be used to compare different data sets, even if they have different numbers of groups.
Applications:
The mean can be used to compare different groups in a data set.
It can be used to calculate the average age of a population of people.
It can be used to assess the central tendency of a data set