Probability
outline is on the side
Histograms and Probability
➔the y-axis would represent relative frequency (more continuous) rather than frequency
➔area of bars determine the probabilities of the scores
❗ side note: when calculating joint probability theyshould (roughly) add up to 1, and will be
symmetrical as you near 1 (normal distribution)
➔in a binomial distribution, the bars get skinner and closer together and start representing a
smooth curve (normal distribution)
Normal Distributions
➔distributions can take on many shapes
◆ normal (AKA Guassian distributions)
◆ bimodal
◆ multimodal
◆ unimodal
◆ positively skewed
◆ negatively skewed
◆ leptokurtic
◆ platykurtic
◆ etc.
➔a normal distribution is characterized by
◆ mean = median = mode
● implies symmetry and unimodal
◆ kurtosis = 0
● nice bell curve shape, not too skinny and not too flat
◆ skew = 0
● tails are symmetrical on both sides
➔what's so special about a normal distribution?
◆ many naturally occurring phenomena are approx. normally distributed
● no matter how big empirical samples of observations are, theynever will be
perfectly normal(even if underlie population is perfectlynormal)
○ assample size increases, the shape will reach approximatenormalitybut
never perfect normality
outline is on the side
Histograms and Probability
➔the y-axis would represent relative frequency (more continuous) rather than frequency
➔area of bars determine the probabilities of the scores
❗ side note: when calculating joint probability theyshould (roughly) add up to 1, and will be
symmetrical as you near 1 (normal distribution)
➔in a binomial distribution, the bars get skinner and closer together and start representing a
smooth curve (normal distribution)
Normal Distributions
➔distributions can take on many shapes
◆ normal (AKA Guassian distributions)
◆ bimodal
◆ multimodal
◆ unimodal
◆ positively skewed
◆ negatively skewed
◆ leptokurtic
◆ platykurtic
◆ etc.
➔a normal distribution is characterized by
◆ mean = median = mode
● implies symmetry and unimodal
◆ kurtosis = 0
● nice bell curve shape, not too skinny and not too flat
◆ skew = 0
● tails are symmetrical on both sides
➔what's so special about a normal distribution?
◆ many naturally occurring phenomena are approx. normally distributed
● no matter how big empirical samples of observations are, theynever will be
perfectly normal(even if underlie population is perfectlynormal)
○ assample size increases, the shape will reach approximatenormalitybut
never perfect normality
