Respuesta :
Answer:
Option b
Step-by-step explanation:
Given : Series 6,2,4,7,3,2.
To find : What is the variance of the series?
Solution :
The variance formula is given by,
[tex]\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex]
Step 1 - The mean of the series,
[tex]\bar{x}=\frac{6+2+4+7+3+2}{6}[/tex]
[tex]\bar{x}=\frac{24}{6}[/tex]
[tex]\bar{x}=4[/tex]
Step 2 - Find [tex]\sum(x_i-\bar{x})^2[/tex]
[tex]\sum(x_i-\bar{x})^2=(6-4)^2+(2-4)^2+(4-4)^2+(7-4)^2+(3-4)^2+(2-4)^2[/tex]
[tex]\sum(x_i-\bar{x})^2=(2)^2+(-2)^2+(0)^2+(3)^2+(-1)^2+(-2)^2[/tex]
[tex]\sum(x_i-\bar{x})^2=4+4+0+9+1+4[/tex]
[tex]\sum(x_i-\bar{x})^2=22[/tex]
Step 3 - Substitute back in formula,
[tex]\sigma^2=\frac{22}{6}[/tex]
[tex]\sigma^2=3.6[/tex]
Therefore, The variance of the series is 3.6.
So, Approximately option b is correct.
