Question

question
find the median and mean of the data set below:
45,8,25,38
answer attempt 1 out of 2
median =
mean =

Explanation:

Step1: Sort the data set

Sort \(45,8,25,38\) in ascending order: \(8,25,38,45\)

Step2: Calculate the median

Since there are \(n = 4\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{4}{2}=2\) and \(\frac{4}{2}+1 = 3\). The median is \(\frac{25 + 38}{2}=\frac{63}{2}=31.5\)

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{1}=8,x_{2}=25,x_{3}=38,x_{4}=45\) and \(n = 4\). \(\bar{x}=\frac{8+25+38+45}{4}=\frac{116}{4}=29\)

Answer:

Median \(=31.5\), Mean \(=29\)