Detailed Summary of Example 7
In this section, we delve into the calculation of the median for grouped data, specifically using cumulative frequency distribution. The median provides a measure of central tendency that identifies the middle value in a dataset.
We begin by constructing a cumulative frequency table for a hypothetical examination score distribution.
The process involves:
1. Identifying the total number of data points (n): In the example, the number of students is noted.
2. Calculating cumulative frequencies for each class interval by summing the frequencies.
3. Determining the median class: This is identified as the class where the cumulative frequency exceeds half of the total data points (n/2).
4. Applying the median formula: We use the formula:
\[ ext{Median} = l + \left( \frac{n/2 - cf}{f} \right) \times h \]
Where:
- l is the lower limit of the median class,
- cf is the cumulative frequency of the class preceding the median class,
- f is the frequency of the median class,
- h is the class size.
5. Interpreting the result: The calculated median value provides insight into the central tendency of student scores in this context, indicating that about half the students scored below the calculated median.
In summary, finding the median for grouped data is crucial for summarizing data distributions, especially when class sizes may vary.