Question

center, spread, and shape of distributions: foundations
3.19, 3.49, 3.79, 3.89, 3.99, 4.19
what is the median of the list of numbers?
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Explanation:

Step1: Determine the number of data points

There are \(n = 6\) numbers in the list \(3.19,3.49,3.79,3.89,3.99,4.19\).

Step2: Use the median formula for an even - numbered data set

For a data set with \(n\) values (where \(n\) is even), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). Here, \(\frac{n}{2}=\frac{6}{2} = 3\) and \(\frac{n}{2}+1=3 + 1=4\).
The third value \(x_3 = 3.79\) and the fourth value \(x_4=3.89\).

Step3: Calculate the median

$$M=\frac{3.79 + 3.89}{2}=\frac{7.68}{2}=3.84$$

Answer:

\(3.84\)