Respuesta :
Answer:
[tex] \bar X = \frac{1+5+8+5+1}{5}= \frac{20}{5}= 4[/tex]
[tex] \sigma= \sqrt{\frac{(1-4)^2 +(5-4)^2 +(8-4)^2 +(5-4)^2 +(1-4)^2}{5}} =\sqrt{\frac{36}{5}}= 2.68[/tex]
And based on this the best answer would be:
a. mean = 4; standard deviation = 2.68
Step-by-step explanation:
For this case we have the following data given:
1,5,8,5,1
We can find the sample mean with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X = \frac{1+5+8+5+1}{5}= \frac{20}{5}= 4[/tex]
And for the deviation (assuming that the correct approximation is the deviation for a population) we can calculate the deviation with the following formula:
[tex] \sigma = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}[/tex]
And replacing we got:
[tex] \sigma= \sqrt{\frac{(1-4)^2 +(5-4)^2 +(8-4)^2 +(5-4)^2 +(1-4)^2}{5}} =\sqrt{\frac{36}{5}}= 2.68[/tex]
And based on this the best answer would be:
a. mean = 4; standard deviation = 2.68
