Question

find the median and mean of the data set below:
38, 32, 27, 14, 31, 50
answer attempt 1 out of 2
median =
mean =

Explanation:

Step1: Sort the data set

Sort the data set \(38, 32, 27, 14, 31, 50\) in ascending order: \(14, 27, 31, 32, 38, 50\).

Step2: Calculate the median

Since there are \(n = 6\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
\(\frac{n}{2}=\frac{6}{2} = 3\), \(\frac{n}{2}+1=4\).
The \(3\)rd value is \(31\) and the \(4\)th value is \(32\).
Median \(=\frac{31 + 32}{2}=\frac{63}{2}=31.5\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n = 6\).
\(\sum_{i=1}^{6}x_{i}=14 + 27+31 + 32+38+50=192\).
Mean \(\bar{x}=\frac{192}{6}=32\).

Answer:

Median \(=31.5\), Mean \(=32\)