Detailed Summary
This section details the concept of the median as a measure of central tendency, specifically for grouped data. The median represents the middle value when data points are organized in ascending order. In grouped data, which is presented in class intervals, direct observation of middle values is not feasible. Thus, the calculation involves constructing cumulative frequency tables.
- Finding the Median:
- Depending on whether the total number of observations (n) is odd or even, the position of the median can be established. If n is even, the median will be the average of the two middle values.
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For grouped data, cumulative frequency distributions are essential. The median class is determined by locating the cumulative frequency that is just greater than or equal to n/2.
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Formula:
The median can be calculated using the formula:
\[
ext{Median} = l + \left(\frac{n/2 - cf}{f} \right) \times h
\]
Where:
- l = lower limit of the median class
- n = total number of observations
- cf = cumulative frequency of the class preceding the median class
- f = frequency of the median class
- h = width of class intervals.
Illustrations in the section demonstrate this procedure using cumulative frequency data to find the median for test scores and heights, underscoring the importance of this statistic in understanding data distributions in various contexts.