If a collection of data has 20 observations, how will the median be calculated?

Answer

To calculate the median of a collection of data with 20 observations, follow these steps:

### Step-by-Step Solution:

1. **Identify the number of observations (n)**:
Here, we have \( n = 20 \).

2. **Determine the position of the median**:
Since the number of observations is even, the median is calculated using the formula:
\[ \text{Median} = \frac{(n/2)^{th} \text{ observation} + ((n/2) + 1)^{th} \text{ observation}}{2} \]

3. **Calculate \( n/2 \)**:
\[ n/2 = 20/2 = 10 \]
So, we need the 10th and 11th observations.

4. **Identify the 10th and 11th observations**:
To find the median, we need to look at the 10th and 11th values in the ordered data set.

5. **Calculate the median**:
The median will be the average of the 10th and 11th observations:
\[ \text{Median} = \frac{\text{10th observation} + \text{11th observation}}{2} \]

### Final Result:
Thus, the median of the data set with 20 observations will be the average of the 10th and 11th observations.

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