 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 -399.319 96.4843 399.106

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.