Answer:
a) 1.9
b) 3.25
c) 1.5
d) -5.25
Step-by-step explanation:
We are given the following in the data:
4, 7, -1, 1, 0, 5, -3, 2, -1, 6, 5, -2
a) Mean change score
![Mean =\displaystyle\frac{23}{12} = 1.9](https://tex.z-dn.net/?f=Mean%20%3D%5Cdisplaystyle%5Cfrac%7B23%7D%7B12%7D%20%3D%201.9)
b) standard deviation for this population
where
are data points,
is the mean and n is the number of observations.
Sum of differences = 126.92
![S.D = \sqrt{\dfrac{126.92}{12}} = 3.25](https://tex.z-dn.net/?f=S.D%20%3D%20%5Csqrt%7B%5Cdfrac%7B126.92%7D%7B12%7D%7D%20%3D%203.25)
c) median change score
Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7
![\text{Median} = \dfrac{6^{th}+7^{th}}{2} = \dfrac{1+2}{2} = 1.5](https://tex.z-dn.net/?f=%5Ctext%7BMedian%7D%20%3D%20%5Cdfrac%7B6%5E%7Bth%7D%2B7%5E%7Bth%7D%7D%7B2%7D%20%3D%20%5Cdfrac%7B1%2B2%7D%7B2%7D%20%3D%201.5)
d) change score that is 2.2 standard deviations below the mean.
![\mu - 2.2(\sigma)\\1.92 - 2.2(3.25) = -5.25](https://tex.z-dn.net/?f=%5Cmu%20-%202.2%28%5Csigma%29%5C%5C1.92%20-%202.2%283.25%29%20%3D%20-5.25)