Studied by 6 peoplepercentile
the pth percentile of a distribution is the value with p% of observations are less than or equal to it
standardized test statistic
AKA z-scores
measures how many standard deviations a data value is above (positive z-score) or below (negative z-score) the mean
has no units
the further from zero it is, the more unusual it is
a z-score of +2 is the boundary for an outlier
a z-score of +3 is the boundary for an extreme outlier
z-score formula
(statistic - parameter)/standard deviation
What does shifting data by adding or subtracting the same number from each observation affect?
mean
median
quartiles
min/max
five-number summary
percentiles
What does shifting data by adding or subtracting the same number from each observation not affect?
standard deviation
range
IQR
shape
What does shifting data by multiplying or dividing the same positive number from each observation affect?
all measures of center and spread
What does shifting data by multiplying or dividing the same positive number from each observation not affect?
shape (may just be more spread out, but remains mostly the same)
density curves
on or above horizontal axis
has an area of exactly 1 underneath the curve
the mean is the point where the curve would balance if made of solid material
the median is the equal-areas point, where the area under the curve is divided in half
What is the shape of the normal distrbution?
symmetric, single-peaked, and bell shaped
free of skew and outliers
How is the center of a normal curve measured?
The mean (μ) is located at the midpoint and is the same as the median
How is the variability of the normal curve measured?
standard deviation (σ) measures the variability, or width
more spread = larger σ and more variability, less spread = smaller σ and less variability
How are normal distributions named?
N (μ,σ)
N (x̄, Sx)
About how much of the data falls within 1 standard deviation of the mean in a normal model?
68%
About how much of the data falls within 2 standard deviations of the mean in a normal model?
95%
About how much of the data falls within 3 standard deviations of the mean in a normal model?
99.7%
The normal model is ________, so we never say 0% or 100%
infinite
How do you find the percentage when z-score is not exactly 1, 2, or 3?
“2nd” > “vars” > “normalcdf”
input the z-score of the lower boundary and the z-score of the upper boundary, then hit “Paste” and then “enter”
How do you find the z-score if you just have the percentile?
“2nd” > “vars” > “invnorm”
input the percentile as a decimal into “area” and choose whether the area is to the left, right, or in the center
Two ways to determine if the normal model is appropriate
Histogram appears unimodal and symmetrical (free of skew and outliers)
Double check by constructing a normal probability plot that should appear roughly linear
How to construct a normal probability plot
Input your data into L1
then “2nd” > “y=”
go to “Plot 1” turn on normal probability plot, then hit “zoom” > “9”
Note
Flashcard