Answer:
A) Private colleges:
mean = 42.7, SD = 6.72
In thousand dollars:
mean = $42700, SD= $6720
B) Public colleges:
mean = 22.3, SD = 4.53
In thousand dollars:
mean = $22300, SD= $4530
Step-by-step explanation:
A) Private Colleges:
Mean:
Total no. of samples = n =10
Sample values in dollar = x= [53.8, 42.2, 44.0, 34.3, 44.0,31.6, 45.8, 38.8, 50.5, 42.0]
Sum of samples = ∑x= 427
![sample\,\,mean = \bar{x} =\frac{\sum x}{n}\\\\\bar{x}=\frac{427}{10}\\\\\bar{x}=42.7\\](https://tex.z-dn.net/?f=sample%5C%2C%5C%2Cmean%20%3D%20%5Cbar%7Bx%7D%20%3D%5Cfrac%7B%5Csum%20x%7D%7Bn%7D%5C%5C%5C%5C%5Cbar%7Bx%7D%3D%5Cfrac%7B427%7D%7B10%7D%5C%5C%5C%5C%5Cbar%7Bx%7D%3D42.7%5C%5C)
Sample mean in thousand dollars is $ 42700.
Standard Deviation:
Formula for standard deviation of sample data is
![\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^2}\\\\\sum(x_i-\bar{x})^2=(53.8-42.7)^2+(42.2-42.7)^2+...+(42.0-42.7)^2\\\\\sum(x_i-\bar{x})^2=123.21+0.25+ 1.69+ 70.56+ 1.69+ 123.21+ 9.61+ 15.21+60.84+0.49\\\\\sum(x_i-\bar{x})^2=406.67\\\\\sigma=\sqrt{\frac{406.67}{9}}\\\\\sigma=6.72](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B1%7D%7BN-1%7D%5Csum_%7Bi%3D1%7D%5E%7BN%7D%28x_%7Bi%7D-%5Cbar%7Bx%7D%29%5E2%7D%5C%5C%5C%5C%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%3D%2853.8-42.7%29%5E2%2B%2842.2-42.7%29%5E2%2B...%2B%2842.0-42.7%29%5E2%5C%5C%5C%5C%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%3D123.21%2B0.25%2B%201.69%2B%2070.56%2B%201.69%2B%20123.21%2B%209.61%2B%2015.21%2B60.84%2B0.49%5C%5C%5C%5C%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%3D406.67%5C%5C%5C%5C%5Csigma%3D%5Csqrt%7B%5Cfrac%7B406.67%7D%7B9%7D%7D%5C%5C%5C%5C%5Csigma%3D6.72)
Standard deviation in thousand dollars is $ 6720.
B) Public Colleges:
Mean:
Total no. of samples = n =12
Sample values in dollar = x= [20.3, 22.0, 28.2, 15.6, 24.1, 28.5,22.8, 25.8, 18.5, 25.6, 14.4, 21.8]
Sum of samples = ∑x= 267.6
![sample\,\,mean = \bar{x} =\frac{\sum x}{n}\\\\\bar{x}=\frac{267.6}{12}\\\\\bar{x}=22.3\\](https://tex.z-dn.net/?f=sample%5C%2C%5C%2Cmean%20%3D%20%5Cbar%7Bx%7D%20%3D%5Cfrac%7B%5Csum%20x%7D%7Bn%7D%5C%5C%5C%5C%5Cbar%7Bx%7D%3D%5Cfrac%7B267.6%7D%7B12%7D%5C%5C%5C%5C%5Cbar%7Bx%7D%3D22.3%5C%5C)
Sample mean in thousand dollars is $ 22300.
Standard Deviation:
![\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^2}\\\\\sum(x_i-\bar{x})^2=(20.3-22.3)^2+(22.0-22.3)^2+...+(21.8-22.3)^2\\\\\sum(x_i-\bar{x})^2=4+ 0.09+34.81+ 44.89+ 3.24+ 38.44+0.25+ 12.25+14.44+10.89+62.41+0.25\\\\\sum(x_i-\bar{x})^2=225.96\\\\\sigma=\sqrt{\frac{225.96}{11}}\\\\\sigma=4.53](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B1%7D%7BN-1%7D%5Csum_%7Bi%3D1%7D%5E%7BN%7D%28x_%7Bi%7D-%5Cbar%7Bx%7D%29%5E2%7D%5C%5C%5C%5C%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%3D%2820.3-22.3%29%5E2%2B%2822.0-22.3%29%5E2%2B...%2B%2821.8-22.3%29%5E2%5C%5C%5C%5C%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%3D4%2B%200.09%2B34.81%2B%2044.89%2B%203.24%2B%2038.44%2B0.25%2B%2012.25%2B14.44%2B10.89%2B62.41%2B0.25%5C%5C%5C%5C%5Csum%28x_i-%5Cbar%7Bx%7D%29%5E2%3D225.96%5C%5C%5C%5C%5Csigma%3D%5Csqrt%7B%5Cfrac%7B225.96%7D%7B11%7D%7D%5C%5C%5C%5C%5Csigma%3D4.53)
Standard deviation in thousand dollars is $ 4530.