Question

1. error analysis brian claims that 2 is the median of the data set shown because it is the middle number. how do you respond to brian? 3, 8, 1, 5, 2, 9, 2, 3, 4

Explanation:

Step1: Order the data set

To find the median, we first need to order the data set from least to greatest. The given data set is \(3, 8, 1, 5, 2, 9, 2, 3, 4\). When we order it, we get \(1, 2, 2, 3, 3, 4, 5, 8, 9\).

Step2: Find the median

For a data set with \(n\) values, if \(n\) is odd, the median is the \(\frac{n + 1}{2}\)-th value. Here, \(n=9\), so \(\frac{9+ 1}{2}=5\)-th value. Looking at the ordered data set \(1, 2, 2, 3, 3, 4, 5, 8, 9\), the 5 - th value is \(3\). Brian made a mistake because he didn't order the data set first before finding the middle number.

Answer:

Brian is incorrect. To find the median, the data set must first be ordered from least to greatest. The ordered data set is \(1, 2, 2, 3, 3, 4, 5, 8, 9\). Since there are 9 (an odd number) of data points, the median is the 5th value, which is \(3\), not \(2\).