For an even number of sorted values, the median is:
AMiddle value
BAverage of the two middle values
CLargest value
DMode
Answer & Solution
Correct answer: B. Average of the two middle values
To find the median of a dataset, the values must first be arranged in ascending or descending order. The median is the central value of the distribution. There are two scenarios based on the number of observations ($n$):
1. **Odd number of values ($n$ is odd):** The median is the single value located at the exact middle position, $\rac{n+1}{2}$.
2. **Even number of values ($n$ is even):** There is no single middle value. Instead, there are two middle values at positions $\rac{n}{2}$ and $\rac{n}{2} + 1$. In this case, the median is calculated as the arithmetic mean (average) of these two middle values.
\nFormula for even $n$:
$$\ ext{Median} = \rac{\ ext{Value at } (n/2) + \ ext{Value at } (n/2 + 1)}{2}$$
\nTherefore, for an even number of sorted values, the median is the average of the two middle values.
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