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Math
Statistics
AP Stats  Chapter 2
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Terms in this set (28)
σ
standard deviation
μ
mean
zscore
a measure of how many standard deviations an individual data point is from the mean
zscore: formula
z = (X  μ) / σ
adding/subtracting a from a distribution
adds/subtracts a from measures of center and location (mean, median, quartiles, percentiles)

does not change
the shape of the distribution or measures of spread (range, IQR, standard deviation)
multiplying/dividing a distribution by b
multiplies/divides measures of center and location (mean, median, quartiles, percentiles) by b
multiplies/divides measures of spread (range, IQR, standard deviation) by b

does not change
the shape of the distribution
invnorm
finds the precise value at a given percentage based upon the mean and standard deviation of a Normal distribution
invnorm function
invnorm(area, mean, SD)
density curve
describes the overall pattern of a distribution
area under the curve and above any interval of values on the horizontal axis is the proportion of all observations that fall in that interval
area under a density curve
1
density curve: median
equalareas point
the point that divides the area under the curve in half
density curve: mean
balance point
the point at which the curve would balance if made of solid material
normalcdf
area under a Normal curve
returns the probability of a single value of the random variable x
normalcdf function
normalcdf(lower, upper, mean, SD)
IQR
Q3  Q1
standard deviation rule
68
95
99.7
standard Normal distribution
mean: 0
SD: 1
The area under a density curve and above any interval of values on the horizontal axis is...
the proportion of all observations that fall in that interval
Chebyshev's inequality
applies to all distributions, not just Normal distributions like the 689599.7 rule
SD = 1(1/k^2)
Normality
being within certain limits that define the range of normal distribution functioning
can be assessed using a Normal Probability Plot
cumulative relative frequency
divide cumulative frequency by total number overall and multiply by 100 to get percent
cumulative frequency
add the counts in the frequency column for the current class and all classes with smaller values of the variable
cumulative relative frequency graph
a plot of the cumulative relative frequency in each class at the smallest value of the next class
can be used to describe the position of an individual within a distribution or locate a specific percentile of the distribution
relative frequency
divide the count in each class by the total number there were and multiply by 100 to get percent
SD of any z distribution
1
Does the transformation from raw score to z score change the shape of the distribution?
no, because it does not change the distance between scores
What do you do if you are trying to find a zscore and the percentages are equidistant?
use larger zscore
formula to find a raw score from a zscore
X = zσ + μ
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