Respuesta :
These are the steps to compute the skew:
- Compute the average of the dataset: sum all of the elements and divide by how many they are:
[tex] \dfrac{1+ 1+ 2+ 2+ 2+ 3+ 3+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 8}{16} = 3.5 [/tex]
- Compute the standard deviation: subtract the average from all elements, square the result, compute the average of this new dataset and take the square root of the result:
When you subtract the mean, you have
-2.5, -2.5, -1.5, -1.5, -1.5, -0.5, -0.5, -0.5, -0.5, 0.5, 0.5, 0.5, 1.5, 1.5, 2.5, 4.5
When you square the results, you have
6.25, 6.25, 2.25, 2.25, 2.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 2.25, 2.25, 6.25, 20.25
The average of this new dataset is
[tex] \sigma^2 = 3.25 [/tex]
Whose square root, i.e. the standard deviation, is
[tex] \sigma = \sqrt{3.25} = 1.8028 [/tex]
- Return to the dataset where you subtracted the mean from each point, and divide each point by the standard deviation:
-1.38675, -1.38675, -0.83205, -0.83205, -0.83205, -0.27735, -0.27735, -0.27735, -0.27735, 0.27735, 0.27735, 0.27735, 0.83205, 0.83205, 1.38675, 2.49615
- Cube these results:
-2.666828, -2.666828, -0.576035, -0.576035, -0.576035, -0.021335, -0.021335, -0.021335, -0.021335, 0.021335, 0.021335, 0.021335, 0.576035, 0.576035, 2.666828, 15.552940
- Sum all these numbers together: the result is 12.289.
- Divide this number by the total number of elements in the dataset:
[tex] \dfrac{12.289}{16} = 0.76805 [/tex]
And this is the skew.
