Median Calculation Steps

To find the median of a set of observations, we first need to arrange the data in ascending order.

The given observations are: 4, 14, 11, 8, 7, 8, 9, 12, 4, 6.

Ordering the Observations

Arranging these numbers from the smallest to the largest, we get:

1. 4
2. 4
3. 6
4. 7
5. 8
6. 8
7. 9
8. 11
9. 12
10. 14

Finding the Median Value

There are 10 observations in total (let's denote this by n, so \(n=10\)). Since n is an even number, the median is the average of the two middle values. The positions of these middle values are calculated as:

• Position 1: \( \frac{n}{2} = \frac{10}{2} = 5 \) (the 5th value)
• Position 2: \( \frac{n}{2} + 1 = \frac{10}{2} + 1 = 5 + 1 = 6 \) (the 6th value)

Looking at our ordered list:

4, 4, 6, 7, 8, 8, 9, 11, 12, 14

The 5th value is 8, and the 6th value is also 8.

Calculating the Median

To find the median, we take the average of these two middle values:

Median = \( \frac{\text{5th value} + \text{6th value}}{2} \)

Median = \( \frac{8 + 8}{2} \)

Median = \( \frac{16}{2} \)

Median = 8

Conclusion

Therefore, the median of the given observations is 8.