The median is the value of the data set that separates the sample in halves.
To determine the median of a determined data set, you have to calculate its position.
The given sample has n=7 elements, to determine the position of the median given that the data set is odd, you have to use the following formula:
[tex]\text{PosMe}=\frac{1}{2}(n+1)[/tex]Replace it with n=7
[tex]\begin{gathered} PosMe=\frac{1}{2}(7+1) \\ \text{PosMe}=\frac{1}{2}\cdot8 \\ \text{PosMe}=4 \end{gathered}[/tex]This result indicates that the media is the fourth observation of the data set.
Next, you have to order the data set from least to greatest:
Original data set: 4, 7, 9, 10, 5, 12, 6
Ordered from least to greatest: 4, 5, 6, 7, 9, 10, 12
Once the data set is ordered, you have to count starting from the left until you reach the fourth observation:
O4, 5, 6, 7, 9, 10, 1
The fourth value of the data set is 7, which means that the median of the data set is 7.
Median=7
2
