AP Statistics 2.1 Notes

Vocabulary flashcards covering percentile concepts, z-scores, and the effects of linear transformations from the 2.1 notes.

Percentile

The pth percentile is the value with p percent of observations below it; data are arranged in order and the percent below a given value is determined; percentiles are read on a graph with data values on the horizontal axis and percentiles on the vertical axis (max 100%).

p-th percentile

The value in a distribution for which p percent of observations are at or below it.

Cumulative Relative Frequency Graph (Ogive)

A graph of the cumulative relative frequency; used to locate percentiles; grows from 0 to 1 (0% to 100%), with steeper segments indicating many observations.

z-score

The number of standard deviations an observation is away from the mean; z = (X − mean) / standard deviation; positive means above the mean, negative means below.

z-score formula

z = (X − mean) / standard deviation.

Add/Subtract a constant (Additive transformation)

Adding or subtracting the same number to every observation shifts the center but does not change the shape or spread of the distribution.

Multiply/Divide by a constant (Multiplicative transformation)

Multiplying or dividing every observation by the same number scales the data, changing center and spread by that factor, but the shape of the distribution remains the same.

Linear transformation

A transformation of the form Y = a + bX; includes additive and multiplicative changes; z-scores are unchanged and the shape of the distribution remains the same.

Mean of the z-score distribution

The average of z-scores is 0 after standardizing.

Standard deviation of the z-score distribution

The spread of z-scores is 1 after standardizing.