Density Curves
Requirements of a density curve
is always on or above the axis
has an area of 1 underneath it
It can look like this
...or this
Standardized Score
commonly referred to as z-scores
this allows you to compare apples and oranges
positive z-score → amount of SD above the mean
negative z-score → amount of SD below the mean
in a normal distribution:
the mean of standardized scores is 0
the standard deviation of standardized scores is 1
For example:
In a distribution with a mean of 4 and a standard deviation of 2. The z-score if the "raw score", or x, is 5 is 0.5, which is also 0.5 standard deviations above the mean.
Percentiles
the pth percentile of a distribution is the value with p percent of the observations less than it
Empirical Rule
for normal distributions only
68-95-99.7
68% of distributions are within 1SD of the mean
95% of distributions are within 2SD of the mean
99.7% of distributions are within 3SD of the mean
