Question

question 4 of 10, step 1 of 1
find the median of the following set of data. round your answer to the nearest hundredth, if necessary.
2, 61, 36, 11, 18, 36
answer
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Explanation:

Step1: Sort the data

First, we sort the given data set \(2, 61, 36, 11, 18, 36\) in ascending order.
Sorting gives us: \(2, 11, 18, 36, 36, 61\).

Step2: Find the median position

The formula for the position of the median in a data set with \(n\) values is:

• If \(n\) is odd, the median is the value at position \(\frac{n + 1}{2}\).
• If \(n\) is even, the median is the average of the values at positions \(\frac{n}{2}\) and \(\frac{n}{2}+ 1\).

Here, \(n = 6\) (which is even). So we need the values at positions \(\frac{6}{2}=3\) and \(\frac{6}{2}+ 1 = 4\).

Step3: Calculate the median

From the sorted data \(2, 11, 18, 36, 36, 61\), the value at position 3 is \(18\) and the value at position 4 is \(36\).
The median is the average of these two values: \(\frac{18 + 36}{2}=\frac{54}{2}=27\).

Answer:

\(27\)