Question

What is the median of the data set 4 7 9 10 5 12 6

Answer 1

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:

`\text{PosMe}=(1)/(2)(n+1)`

Replace it with n=7

`\begin{gathered} PosMe=(1)/(2)(7+1) \\ \text{PosMe}=(1)/(2)\cdot8 \\ \text{PosMe}=4 \end{gathered}`

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

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