Respuesta :
Answer:
[tex] E(X) = \frac{431.5}{49}= 8.81[/tex]
[tex] s^2 = \frac{4780.25- \frac{(431.5)^2}{49}}{48} = 20.425[/tex]
[tex] s= \sqrt{20.425}= 4.52[/tex]
Step-by-step explanation:
For this case we can calculate all the questions with the following table:
Class Midpoint(Xi) fi Xi*fi Xi^2 *fi
____________________________________
0-3 1.5 6 9 13.5
3-6 4.5 6 27 121.5
6-9 7.5 11 82.5 618.75
9-12 10.5 21 220.5 2315.25
12-25 18.5 5 18 1711.25
_____________________________________
Total 49 431.5 4780.25
We can calculate the expected value with the following formula:
[tex] E(X) = \frac{\sum_{i=1}^n X_i P(X_i)}{n}[/tex]
And if we replace we got:
[tex] E(X) = \frac{431.5}{49}= 8.81[/tex]
We can calculate the sample variance with the following formula:
[tex] s^2 =\frac{\sum X^2 f -\frac{(\sum xf)^2}{n} }{n-1}[/tex]
And replacing we got:
[tex] s^2 = \frac{4780.25- \frac{(431.5)^2}{49}}{48} = 20.425[/tex]
And the deviation would be just the square root of the variance like this:
[tex] s= \sqrt{20.425}= 4.52[/tex]
