Question

what is the difference between the mean and the median of the data set? {22, 8, 10, 18, 12, 20}
options: 0, 2, 4, 6

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a data - set $\{x_1,x_2,\cdots,x_n\}$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
For the data - set $\{22,8,10,18,12,20\}$, $n = 6$ and $\sum_{i=1}^{6}x_i=22 + 8+10 + 18+12+20=90$.
So, the mean $\bar{x}=\frac{90}{6}=15$.

Step2: Calculate the median

First, sort the data - set: $\{8,10,12,18,20,22\}$.
Since $n = 6$ (an even number), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
Here, $x_{\frac{n}{2}}=x_3 = 12$ and $x_{\frac{n}{2}+1}=x_4 = 18$.
So, the median $M=\frac{12 + 18}{2}=15$.

Step3: Calculate the difference

The difference between the mean and the median is $|15-15| = 0$.

Answer:

0