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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.