Answer:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \abr X = \frac{15+25+25+25}{4}= 20 \%[/tex]
And now we can calculate the variance like this:
[tex] s^2 = \frac{(15-20)^2 +(25-20)^2 +(25-20)^2 +(15-20)^2}{4-1}= \frac{100}{3}= 33.33[/tex]
And the deviation is just the square root of the variance and we got:
[tex] s = \sqrt{33.33}= 5.77 \%[/tex]
Explanation:
For this case we have the following data:
15%, 25%, 25%, and 15%
So for this case n = 4
And we can calculate the sample variance with the following formula:
[tex] s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
First we need to calculate the mean with this formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \abr X = \frac{15+25+25+25}{4}= 20 \%[/tex]
And now we can calculate the variance like this:
[tex] s^2 = \frac{(15-20)^2 +(25-20)^2 +(25-20)^2 +(15-20)^2}{4-1}= \frac{100}{3}= 33.33[/tex]
And the deviation is just the square root of the variance and we got:
[tex] s = \sqrt{33.33}= 5.77 \%[/tex]
