What Is Grouped Data?
When we collect large amounts of numerical data, it's often impractical to list every single value. Instead, we organize the data into groups (also called class intervals or bins). This is called grouped data.
For example, if you measured the heights of 100 students, instead of listing all 100 individual heights, you might group them:
| Height (cm) | Frequency |
|---|---|
| 140–149 | 12 |
| 150–159 | 28 |
| 160–169 | 35 |
| 170–179 | 18 |
| 180–189 | 7 |
Data that has been organized into class intervals (groups), where each interval covers a range of values and has an associated frequency.
A range of values that defines each group in a grouped frequency table. For example, 140–149 is a class interval with a width of 10.
The number of data values that fall within a particular class interval.
Once data is grouped, we lose the individual values. We can no longer know the exact data points — only how many fall in each interval. This means our measures of central tendency will be estimates, not exact values.
The Midpoint of a Class Interval
Since we don't know the exact values within each group, we use the midpoint (also called the mid-interval value) to represent all the data in that group.
The middle value of a class interval, calculated by averaging the lower and upper boundaries:
The midpoint is our best estimate for the "typical" value in each interval.
Finding midpoints
For the class interval 140–149:
For the class interval 150–159:
For the class interval 160–169:
A quick shortcut: just add the lower and upper values and divide by 2. You can also add half the class width to the lower boundary — both methods give the same answer!
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