Question

find the median and mean of the data set below:
41, 13, 49, 45, 31, 16
answer attempt 1 out of 2
median =
mean =

Explanation:

Step1: Find the median

First, we need to sort the data set in ascending order. The data set is \(41, 13, 49, 45, 31, 16\). Sorting it gives us \(13, 16, 31, 41, 45, 49\). Since there are 6 (an even number) data points, the median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th numbers, which are \(31\) and \(41\). So, the median is \(\frac{31 + 41}{2}=\frac{72}{2} = 36\).

Step2: Find the mean

The mean is calculated by summing all the data points and then dividing by the number of data points. The sum of the data points is \(41+13 + 49+45+31+16\). Let's calculate that: \(41+13 = 54\), \(54+49 = 103\), \(103+45 = 148\), \(148+31 = 179\), \(179+16 = 195\). There are 6 data points, so the mean is \(\frac{195}{6}=32.5\).

Answer:

Median = \(36\), Mean = \(32.5\)