Question

consider the data set
8 6 9 4 1 9
find the average (mean):
find the median:
question help: video 1 video 2

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 6$, and $x_{1}=8,x_{2}=6,x_{3}=9,x_{4}=4,x_{5}=1,x_{6}=9$. Then $\sum_{i=1}^{6}x_{i}=8 + 6+9+4+1+9=37$. So, $\bar{x}=\frac{37}{6}\approx6.17$.

Step2: Calculate the median

First, sort the data set: $1,4,6,8,9,9$. Since $n = 6$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. So, $M=\frac{6 + 8}{2}=7$.

Answer:

6.17, 7