Question

find the median and mean of the data set below: 40, 8, 31, 3 answer attempt 1 out of 2 median = mean =

Explanation:

Step1: Sort the data set

Sort the data set \(3,8,31,40\).

Step2: Calculate the median

Since there are \(n = 4\) data points (even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values. \(\frac{n}{2}=2\), \(\frac{n}{2}+1 = 3\). The median is \(\frac{8 + 31}{2}=\frac{39}{2}=19.5\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 4\), \(x_1=3\), \(x_2 = 8\), \(x_3=31\), \(x_4=40\). \(\sum_{i=1}^{4}x_{i}=3 + 8+31 + 40=82\). The mean is \(\frac{82}{4}=20.5\).

Answer:

Median \(=19.5\), Mean \(=20.5\)