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Consider the frequency distribution table.
| Height (in m) | \(30 - 40\) | \(40 - 50\) | \(50 - 60\) | \(60 - 70\) | \(70 - 80\) |
| Number of trees | \(124\) | \(156\) | \(200\) | \(10\) | \(10\) |
The above frequency table shows that the data are grouped in class intervals. This table shows that the number of trees with various heights.
Consider the interval \(50 - 60\). There are \(200\) trees in the heights between \(50 - 60\) metres. In grouped frequency, the individual observations are not available. Thus, we need to determine the value that indicates the particular interval. This value is called a midpoint or class mark. The midpoint can be determined using the formula:
Midpoint \(= \frac{UCL + LCL}{2}\)
Where \(UCL\) is the upper class limit and \(LCL\) is the lower class limit.
Example:
Consider the interval \(40 - 50\). Let us find the midpoint of this interval.
Here, \(UCL = 40\) and \(LCL = 50\)
Midpoint of \(40 - 50\) is \(\frac{40 + 50}{2} =\) \(\frac{90}{2}\) \(= 45\)
Therefore, the midpoint of the interval \(40 - 50\) is \(45\).
The arithmetic mean of a grouped frequency distribution can be determined using any one of the following methods.
- Direct method
- Assumed mean method
- Step deviation method
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