Standard deviation measures the spread of scores within a data set. It measures the dispersion of a dataset relative to its means, and it is calculated as the square root of the variance. It helps determine the point of deviation to the mean. When data points are far from the mean, there is a higher deviation within that particular data set. The more the data set is spread, the higher the standard deviation.

## Conditional means and standard deviation

The average cost per bachelor’s degree for private is $523.23 and the variation around the mean is$1,431.54 while the average cost per bachelor’s degree for the public is $37.96 and the variation around the mean is$130.28. The result shows that the return on investment is higher for private than public by $485.27. The variation is also higher for private than public.  Associates Baccalaureate Doctoral Masters Special Focus Tribal Mean 816.22 160.57 34.29 57.84 1159.25 415.85 Std. Deviation 1740.78 205.68 133.37 88.87 2191.21 605.34 From the result above, we see that special focus has the highest return on investment of$1159.25 followed by Associates with a return on investment of $816.22. Doctoral have the lowest return to investment of$34.29. The variation in return on investment follows the same pattern.

## Correlation

The scatter plot suggests a weak negative relationship between returns on education and tuition fees. The correlation coefficient is -0.078 (p<0.0001) which means a weak negative but significant relationship exists between returns on education and tuition fees. The coefficient of determination is 0.006 which means only 0.6% of the variation in returns to education is explained by tuition fees.

From the analysis so far, we see that private universities provide the best return on investment, similarly, universities whose Carnegie classification is special focus provides the best return on investment. More expensive institutions also provide a better return on investment compared to less expensive ones.

## Crosstabulation

 Carnegie * sector Crosstabulation sector Total Private Public Carnegie Associates Count 338 979 1317 % within sector 13.2% 61.0% 31.7% Baccalaureate Count 438 88 526 % within sector 17.1% 5.5% 12.6% Doctoral Count 134 192 326 % within sector 5.2% 12.0% 7.8% Masters Count 466 269 735 % within sector 18.2% 16.8% 17.7% Special Focus Count 1172 49 1221 % within sector 45.9% 3.1% 29.4% Tribal Count 8 27 35 % within sector 0.3% 1.7% 0.8% Total Count 2556 1604 4160 % within sector 100.0% 100.0% 100.0%
From the result above, we see that slightly below half of the private universities have Carnegie classification of special focus while 61% of public universities have Carnegie classification of associates. The percent of masters are similar for both private and public universities. The result suggests there is an association between Carnegie classification and sector.

## Return on investment

I will do in addition to what has been done significance test of difference in mean returns (independent t-test for the sector, one way ANOVA for Carnegie classification. Finally, I will conduct regression to estimate the specific effect of tuition fees on return on investment.
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