AP Statistics 2.1 - Describing Location in a Distribution

percentile

the percent of values in a distribution that are less than the individual's data value.

cumulative relative frequency graph

plots a point corresponding to the cumulative relative frequency in each interval at the smallest value of the next interval, starting with a point at a height of 0% at the smallest value of the first interval. Consecutive points are then connected with a line segment to form the graph.

z-score

standardized score; tells us how many standard deviations from the mean an observation falls, and in what direction.

standardized score of x

z = (value - mean) / standard deviation

effect of adding or subtracting a constant

Adds a to (subtracts a from) measures of center and location (mean, five-number summary, percentiles)
Does not change measures of variability (range, IQR, standard deviation)
Does not change the shape of the distribution

effect of multiplying or dividing a constant

Multiplies (divides) measures of center and location by b (mean, five-number summary, percentiles) by b
Multiplies (divides) measures of variability by b (range, IQR, standard deviation)
Does not change the shape of the distribution

error

error = guess - actual value