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```AP Review
Exploring Data
Describing a Distribution
Discuss center, shape, and spread in context.
Center: Mean or Median
Shape: Roughly Symmetrical, Right or Left
Skewed
Spread: Standard Deviation, IQR, Range, or
Checking for Outliers
A survey was conducted to gather ratings of the
quality of service at local restaurants at a
nearby mall. Respondents were to rate overall
service using values between 0 (terrible) and
100 (excellent). The five number summary is
32, 47.5, 51, 63.5, 92. The data values above
Q3 are 65, 66, 70, 71, and 92. Are there
outliers on the high end?
Checking for Outliers
Outliers > Q3 + 1.5(IQR)
Outliers > 63.5 + 1.5 (63.5 – 47.5)
Outliers > 87.5
Therefore, 92 is an outlier.
Robust and Sensitive Statistics

Robust (not affected by extreme values)
Median, IQR

Sensitive (affected by extreme values)
Mean, s, range
Parameters and Statistics

Parameters are numerical values that describe
a population.

Statistics are numerical values that describe a
sample.
Z – Scores and Percentiles


Barron’s p. 41 #10
Assuming that batting averages have a bellshaped distribution, arrange in ascending
order:
I. An average with a z-score of –1
II. An average with a percentile rank of 20%.
III. An average at the first quartile, Q1.
I, II, III
Normal Distribution


Barron’s P. 367 #3
The average yearly snowfall in a city is 55
inches. What is the standard deviation if 15%
of the years have snowfalls above 60 inches?
Assume yearly snowfalls are normally
distributed.
z
x

  4.83
1.036 
60  55

Linear Regression




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
Don’t forget about formulas on chart.
r is the correlation coefficient.
r^2 is the coefficient of determination.
r has no units
Strong r indicates association, not causation.
r is not affected if x & y are reversed or if
operations (mult, divide, add, sub) are
performed on each x or on each y.
 x , y  is always on yˆ  a  bx
Linear Regression


r^2 describes the percent variation of the
dependent variable, y, explained by the linear
relationship (LSRL) with the independent
variable, x. PUT IN CONTEXT!
When discussing r, describe line as weak,
moderate, or strong linear relationship between
x&y
Linear Regression


Influential Point – pulls regression line toward
it. An influential point is usually a point in the xdirection.
Outlier – shows up in residual plot usually in
the y – direction.
Linear Regression

When performing Linear Regression, do the
following:
Create a scatterplot
Calculate the equation of the regression line
Plot the residuals
A residual is the observed y – predicted y.
Barron’s Problems
Multiple Choice
P. 370 #13, 14, 16, 19, 21, 24, 27, 30, 38

Free Response
P. 430 #2

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