AP Stats: Chapter 2

if someone scored at the 93rd percentile, that means that in the distribution, 93% of the people earned that score or less

(number of scores below the score) / (total number of scores)

used to examine a location within a distribution. Groups the observations into equal-width classes, shows accumulating percent of observations as you move through the classes in increasing order

(frequency)/(total frequencies) x100

(frequency) + (frequencies below this frequency)

(cumulative frequency)/(total frequencies)

cumulative relative frequency graph aka ogive

percentage represents the amount of people at that class or lower

aka cumulative relative frequency graph

• adds a to the center and location (mean, median, quartiles, percentiles)
• does not affect shape or measures of spread (range, IQR, standard deviation)

• multiplies/divides measures of center and location by b (mean, median, quartiles, percentiles)
• multiplies/divides measures of spread by |b| (range, IQR, standard deviation)
• multiplies/divides the variance by b²
• does not change shape

• a curve that is always on or above the horizontal axis and has exactly 1 area underneath it
• describes the overall pattern of a distribution

point with half the area under the curve to its left and  the remaining half of the area to its right, divides the area of the density curve in half

the point at which the curve would balance if made of solid material

• described by the normal density curve, specified by the mean and standard deviation N (μ, σ)
• mean is at the center of the symmetric normal curve, standard deviation is the distance from the center to the change-of-curvature points on each side

point where the curve changes shape; where the curve changes from a right-side up U to an upside down U

• scores on tests taken by many people
• repeated careful measurement of same quantity
• characteristics of biological populations

68-95-99.7 Rule

in any distribution, the proportion of observations falling within k standard deviations of the mean is at least

normal distribution with a mean 0 and standard deviation 1

standard normal distribution

table of areas under the standard normal curve; table entry for each value z is the area to the left of z; shown in Table A

normal probability plot

used to assess whether a data set follows a normal distribution

• normal if points lie close to a straight line
• clear departures from normality indicate that the data is not normal

calculator function used to find the area of a normal distribution when you have the cutoff points

calculator function used to find the associated cutoff points when you have the area