Distribution and SD
Standard deviation (pop) ^2 = sum of [(x (value)-mean) ^2/N (number of observations)
Standard deviation (sample) ^2 = sum of [(x (value)-mean) ^2/n-1 (s =)
Symmetric Distribution- the mean and median are equal and the data values are e
Coefficient of Variation
Know the use of the coefficient of variation- in case of more than one mean, and one standard
deviation, we find the coefficient of variation and use this to compare the variability amongst
populations or samples
Population C.V. =
Binomial Distribution
Binomial distribution- a widely occurring discrete probability distribution
Four characteristics of a binomial setting- 1. Fixed number of observations 2. Each observation
falls into one of two outcomes (success, failure) 3. Each obs
Box PlotsQ1 = (n+1) * .25
Q3 = (n+1) * .75
Low outlier < Q1-[1.5(Q3-Q1)]
High outlier > Q3 + [1.5(Q3-Q1)]
Five Number Summary-Min, Q1, Median, Q3, Max
Standard deviation (pop) ^2 = sum of [(x (value)-mean) ^2/N (number of observations)
Standard deviation
Probability
Probability- a value between zero and one, inclusive, describing the relative possibility (chance
or likelihood) an event will occur. Chance behavior is unpredictable in the short run, but has
regular and predictable patterns in the long run.
Probability Distribution
Characteristics of a normal p.d. and the 2 parameters that define it- 1. It is bell-shaped and has a
single peak at the center of the distribution, the mean, median, and mode are equal and located at
the center of the distribution
Other
Why is the mean also called the Expected Value? It is the weighted average where the possible
values of a random variable are weighted by their corresponding probabilities of occurrence.
Empirical Rule
For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations
will lie within plus and minus one standard deviation of the mean; about 95% of the observations
will lie within plus and minus two standard deviat