Question

find the median and mean of the data set below:
38, 16, 37, 29
answer attempt 1 out of 2
median =
mean =

Explanation:

Step1: Sort the data set

Sort \(38,16,37,29\) in ascending order: \(16,29,37,38\)

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 values are \(29\) and \(37\). Median\(=\frac{29 + 37}{2}=\frac{66}{2}=33\)

Step3: Calculate the mean

Mean\(=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{1}=16,x_{2}=29,x_{3}=37,x_{4}=38\) and \(n = 4\). \(\sum_{i=1}^{4}x_{i}=16 + 29+37 + 38=120\). Mean\(=\frac{120}{4}=30\)

Answer:

Median = \(33\), Mean = \(30\)