Subjects statistics

Median Grouped 1Ec269

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1. **Problem Statement:** Calculate the median of grouped data using the formula and understand its components. 2. **Formula for Median of Grouped Data:** $$\text{Median} = L + \left(\frac{\frac{n}{2} - F}{f}\right) \times h$$ 3. **Explanation of Components:** - $L$: Lower boundary of the median class (the class interval containing the median). - $n$: Total number of observations (sum of all frequencies). - $F$: Cumulative frequency of the class before the median class. - $f$: Frequency of the median class. - $h$: Width of the median class interval. 4. **Steps to Calculate Median:** - Find $n$, the total frequency. - Calculate $\frac{n}{2}$. - Identify the median class: the class where cumulative frequency just exceeds $\frac{n}{2}$. - Note $L$, $F$, $f$, and $h$ for the median class. - Substitute values into the formula and simplify. 5. **Interpretation:** The formula adjusts the lower boundary $L$ by a fraction of the class width $h$ based on how far $\frac{n}{2}$ is into the median class, giving an estimate of the median value within grouped data.