How to calculate median for grouped data?
Understand the Problem
The question is asking for a method to calculate the median in the context of grouped data, which typically requires understanding the cumulative frequency and the class intervals of the data. The high-level approach would involve identifying the median class and applying the formula for median calculation for grouped data.
Answer
L + \left( \frac{\frac{n}{2} - CF}{f} \right) \times h
Answer for screen readers
The final answer is the median calculated using the provided formula
Steps to Solve
- Identify the median class
To find the median class, you need to look at the cumulative frequencies. The median class is the class interval where the median lies. First, find the total number of data points ($n$) and then calculate $\frac{n}{2}$. The median class is the class where the cumulative frequency just exceeds $\frac{n}{2}$.
- Apply the median formula
Once you have identified the median class, use the following formula to calculate the median:
$$ \text{Median} = L + \left( \frac{\frac{n}{2} - CF}{f} \right) \times h $$ where:
- $L$ is the lower boundary of the median class
- $n$ is the total number of observations
- $CF$ is the cumulative frequency of the class preceding the median class
- $f$ is the frequency of the median class
- $h$ is the class width
- Substitute values into the formula
Plug in the appropriate values for $L$, $\frac{n}{2}$, $CF$, $f$, and $h$ obtained from the previous steps into the formula to calculate the median.
The final answer is the median calculated using the provided formula
More Information
The formula for calculating the median in grouped data helps provide a central tendency measure even when raw data is not available.
Tips
A common mistake is to incorrectly identify the median class by not properly calculating $\frac{n}{2}$ or cumulative frequency. Always double-check your cumulative frequency table.
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