Question

question 5 of 10, step 1 of 1
find the median of the following set of data. round your answer to the nearest hundredth, if necessary.
78.7, 75.5, 85.3, 34.2, 39.3, 78.9
answer
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Explanation:

Step1: Order the data

First, we need to sort the given data set in ascending order. The data set is \(78.7, 75.5, 85.3, 34.2, 39.3, 78.9\). Sorting them gives: \(34.2, 39.3, 75.5, 78.7, 78.9, 85.3\).

Step2: Find the median position

For a data set with \(n\) values, if \(n\) is even, the median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+1)\)-th values. Here, \(n = 6\) (even), so \(\frac{n}{2}=3\) and \(\frac{n}{2}+1 = 4\).

Step3: Calculate the median

The 3rd value is \(75.5\) and the 4th value is \(78.7\). The median is the average of these two values: \(\frac{75.5 + 78.7}{2}=\frac{154.2}{2}=77.1\).

Answer:

\(77.1\)