To find the range in a grouped frequency table, subtract the lower limit of the lowest class interval from the upper limit of the highest class interval.
Here's a breakdown:
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Identify the lowest class interval: This is the interval with the smallest values. Find the lower limit of this interval.
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Identify the highest class interval: This is the interval with the largest values. Find the upper limit of this interval.
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Calculate the range: Subtract the lower limit of the lowest class from the upper limit of the highest class.
Formula:
Range = (Upper Limit of Highest Class) - (Lower Limit of Lowest Class)
Example:
Consider the following grouped frequency table:
| Class Interval | Frequency |
|---|---|
| 0-10 | 5 |
| 10-20 | 12 |
| 20-30 | 18 |
| 30-40 | 8 |
| 40-50 | 2 |
- Lowest Class Interval: 0-10. The lower limit is 0.
- Highest Class Interval: 40-50. The upper limit is 50.
- Range: 50 - 0 = 50
Therefore, the range of this grouped frequency table is 50.
Important Considerations:
- This method provides an estimate of the range. Since the individual data points within each class interval are unknown, the true range could be slightly different.
- This calculation only works for continuous data grouped into class intervals.
