1. 3 common measures of dispersion or variability Range Range Variance Variance Standard Deviation Standard Deviation

2. Range (Highest value) – (Lowest Value) (Highest value) – (Lowest Value) Quick & easy, but only reflects the extremes, and may be distorted by one extreme value. Quick & easy, but only reflects the extremes, and may be distorted by one extreme value.

3. Variance and Standard Deviation

4. Standard Deviation Standard Deviation of the Population is designated with the lower case of the Greek letter, sigma. It looks like our “o” with a tail on top. σ Standard Deviation of the Population is designated with the lower case of the Greek letter, sigma. It looks like our “o” with a tail on top. σ Standard Deviation of the Sample is designated with the lower case of our usual letter, s. Standard Deviation of the Sample is designated with the lower case of our usual letter, s.

5. Variance Variance of the Population is the square of the standard deviation, so it is designated with the lower case sigma, squared. σ 2 Variance of the Population is the square of the standard deviation, so it is designated with the lower case sigma, squared. σ 2 Variance of the Sample is similarly designated with the lower case s, squared. s 2 Variance of the Sample is similarly designated with the lower case s, squared. s 2

6. Standard Deviation: Computational Formula Standard deviation is the square root of the variance, and Standard deviation is the square root of the variance, and Variance is the square of the standard deviation. Variance is the square of the standard deviation.

7. Standard Deviation Represents a sort of average variability, or deviation, from the mean a sort of average variability, or deviation, from the mean is in the same units as the mean. is in the same units as the mean.

8. Standard Deviation If the mean = 80, and s = 5, that means one standard deviation is 5 units from the mean of 80. If the mean = 80, and s = 5, that means one standard deviation is 5 units from the mean of 80. If we are measuring length, the mean might be 80 ft, and s is then 5 ft. If we are measuring length, the mean might be 80 ft, and s is then 5 ft. If we are measuring scores, the mean might be 80 points and s is 5 points. If we are measuring scores, the mean might be 80 points and s is 5 points.

9. Standard Deviation This would be reported by saying the mean is 80 plus or minus a standard deviation of 5. This would be reported by saying the mean is 80 plus or minus a standard deviation of 5. A little more than 2/3 of the values in a normal distribution will be within 1 standard deviation above and below the mean, here between 75 and 85. A little more than 2/3 of the values in a normal distribution will be within 1 standard deviation above and below the mean, here between 75 and 85.

11. For mean of 120, with sd of 25,