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

how to calculate percentile from data
(number of scores below the score) / (total number of scores)

cumulative relative frequency graph
used to examine a location within a distribution. Groups the observations into equalwidth classes, shows accumulating percent of observations as you move through the classes in increasing order

how to calculate relative frequency
(frequency)/(total frequencies) x100

how to calculate cumulative frequency
(frequency) + (frequencies below this frequency)

how to calculate cumulative relative frequency
(cumulative frequency)/(total frequencies)

cumulative relative frequency graph aka ogive

interpretation of cumulative relative frequency
percentage represents the amount of people at that class or lower

ogive
aka cumulative relative frequency graph

how to calculate zscores

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

effect of multiplying or dividing by a constant
 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 b^{2}^{}
 does not change shape

density curve
 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

median of a density curve
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

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

normal distribution
 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 changeofcurvature points on each side

inflection point
point where the curve changes shape; where the curve changes from a rightside up U to an upside down U

common examples of normal distributions
 scores on tests taken by many people
 repeated careful measurement of same quantity
 characteristics of biological populations


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

standard normal distribution
normal distribution with a mean 0 and standard deviation 1

standard normal distribution

standard normal table
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

how to use a normal probability plot to tell if something is a normal distribution
 normal if points lie close to a straight line
 clear departures from normality indicate that the data is not normal

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

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

