1. Measures of Spread The Range, Variance, and Standard Deviation

2. Range

3. Variance

4. Standard Deviation

5. Example with n = 10 Case number (i)Value of X (X i ) 15 21 39 45 55 67 75 85 95 103

6. Find Squared Deviations i XiXi X i – MeanSquared Difference 15 0 0 21 – 4 16 39 4 45 0 0 55 0 0 67 2 4 75 0 0 85 0 0 95 0 0 103 – 2 4

7. Variance, SD, Range The Variance is the sum of Squared Deviations about the Mean, divided by the number of scores. In this example, the sum of Squared Deviations (Errors) is 40. Divided by n = 10, the Variance of X is 4. The Standard Deviation is the square root of the variance, or 2. The Range is 9 – 1 = 8.

8. Next Topic: z-scores Once we know the variance, we compute the standard deviation. With the mean and standard deviation, we can compute z-score for each value of X. These standard scores measure the relation between each score and its distribution.