Question

find the median and mean of the data set below:
47, 15, 6, 49, 45, 30
answer attempt 1 out of 2
median =
mean =

Explanation:

Step1: Sort the data set

Sort the data set \(47, 15, 6, 49, 45, 30\) in ascending order: \(6, 15, 30, 45, 47, 49\).

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 median \(M=\frac{30 + 45}{2}=\frac{75}{2}=37.5\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n = 6\).
\(\sum_{i=1}^{6}x_{i}=6 + 15+30 + 45+47+49=192\).
\(\bar{x}=\frac{192}{6}=32\).

Answer:

Median \(=37.5\), Mean \(=32\)