Example Question:
2. Using the definitional formulas, find the mean, standard deviation, and variance of the population from which the following sample of data was randomly drawn. The data represents the dementor scores of the patients in dementor units. Please show all work and round to four decimal places.
-118 | -399.3190 | 96.4843 | 399.1058 |
Example Answer:
| Score | Score - Mean = Deviation | Deviation Squared |
| -117.9998 | -117.9998 - -5.4323 = -112.5675 | 12671.4421 |
| -399.3194 | -399.3194 - -5.4323 = -393.8871 | 155147.0475 |
| 96.4843 | 96.4843 - -5.4323 = 101.9166 | 10386.9934 |
| 399.1058 | 399.1058 - -5.4323 = 404.5381 | 163651.0744 |
Sum = | -21.7291 | 0.0001 | 341856.5574 |
Mean = -21.7291/4 = -5.4323
Sample Variance = 341,856.5574/3 = 113,952.1858
Sample Standard Deviation = 
337.5680
Example Explanation:
- First, sum up the scores and divide by n to find the mean.
- Next, subtract the mean from each score to find the deviation.
- Square each deviation.
- Sum the squared deviations.
- To get the sample variance, divide the sum of squared deviations by N - 1
- To get the sample standard deviation, square root the sample variance.