AP Stats Unit 2 Review

percentile

percentile

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?

1. mean

2. median

3. quartiles

4. min/max

5. five-number summary

6. percentiles

What does shifting data by adding or subtracting the same number from each observation not affect?

1. standard deviation

2. range

3. IQR

4. 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”