1. Ignore parts with eye-ball estimation & computational formula
Measures of Variation
Chapter 5
Homework: 1- 6
Ignore parts with eye-ball estimation
& computational formula

2. Variation Width of distribution how much values of variable differ
Independent of central tendency
Measures
range
standard deviation
variance ~

3. Which one do we use? Level of measure determines nominal ordinal
interval/ratio

4. Range Simplest measure of variation depends on only 2 points of data
Distance between highest & lowest value
range = highest - lowest
Same range, very different distributions
2, 6, 6, 6, 6, 6, 10
2, 2, 2, 6, 10, 10, 10 ~

5. SS s2 s SS, s2, & s Other measures of variation related
sums of squares
variance
standard deviation
All data points represented
Mean Squared Deviations Formula
Computational formula not covered SS s2 s

6. Deviation Distance of any point from mean error
Sample: deviationi = Xi - X
Population: deviationi = Xi - m ~

7. Sums of Squares (SS) Sum of squared deviations
S (distance of each point from mean)2

8. Variance Mean of squared deviations s 2, s2
n - 1 : s2 underestimated for sample
correction factor: increases s2
degrees of freedom ~

9. Standard Deviation Square root of variance s , s Mean deviation
why use squared deviations ~

10. Inflection Points of Normal Distributions
Point on curve where curvature changes
upward to downward
downward to upward
normal curve: 2 inflection points
no matter width ~

11. Inflection Points of Normal Distributions
Wider distribution:
inflection points farther from mean
Standard deviation equals
Distance from inflection point to mean
normal distribution only
Can obtain rough estimate
avoid large mistakes ~

12. Inflection Points of Normal Distributions