Answer:
[tex] s= \sqrt{80.568}=8.97 [/tex]
[tex] Median =\frac{1+3}{2}=2[/tex]
Step-by-step explanation:
For this case we have the following data:
1.0 -5 3.0 -8 14 -11 12 0 16 -2 12 7
And ordering this data we have:
-11 -8 -5 -2 0 1 3 7 12 12 14 16
And we are interested in find the standard deviation for the sample data. In order to do this the first step is find the mean given by this formula:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}=\frac{1-5+3-8+14-11+12+0+16-2+12+7}{12}=3.25[/tex]
Now with the sample mean 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]
And if we replace we got:
[tex] s^2 =80.568[/tex]
And for the sample deviation we just need to take the square root of the sample variance and we got:
[tex] s= \sqrt{80.568}=8.97 [/tex]
The median on this case would be given by:
[tex] Median =\frac{1+3}{2}=2[/tex]
Using the positions 5 and 6 for the average since the sample size is an even number.
