Question

question 8 of 10, step 1 of 1
find the median of the following set of data. round your answer to the nearest hundredth, if necessary.
68, 90.2, 63, 68.1, 9.6, 2
answer
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Explanation:

Step1: Sort the data set

First, we need to sort the given data set in ascending order. The data set is \(68, 90.2, 63, 68.1, 9.6, 2\). Sorting them gives: \(2, 9.6, 63, 68, 68.1, 90.2\).

Step2: Determine the median position

The number of data points \(n = 6\), which is even. For an even number of data points, the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+ 1)\)-th values. Here, \(\frac{n}{2}=\frac{6}{2}=3\) and \(\frac{n}{2}+ 1=4\).

Step3: Find the median

The 3rd value in the sorted data set is \(63\) and the 4th value is \(68\). The median is the average of these two values, so we calculate \(\frac{63 + 68}{2}=\frac{131}{2}=65.5\).

Answer:

\(65.5\)