AP Statistics
Chapter 2 Outline
Assignments:
Wed, 9/2
2.1 #5-23 odd, 31
Fri 9/5
2.2 #41-59 odd
Wed 9/9
2.2 #63, 65, 66, 68, 69-74
Mon 9/14
Review Assignment
Wed 9/16
Chapter 2 Test
2.1 Describing Location in a Distribution
 Measure position using percentiles
 Interpret cumulative relative frequency graphs
 Measure position using z-scores
 Transform data
 Define and describe density curves
2.2 Normal Distributions
 Describe and apply the 68-95-99.7 Rule
 Describe the standard Normal Distribution
 Perform Normal distribution calculations
 Assess Normality
 Draw and find areas under a standard Normal Curve
 Create Normal Probability Plot for a set of quantitative data
2.1 Describing Location
Percentile (Measuring Relative Standing)


The pth percentile of a distribution is
____________________________________________________________________________________
____________________________________________________________________________________
Often used when reporting academic scores such as SAT scores
If you are trying to find the percentile corresponding to a certain score x:
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒 =
∙ 100
Cumulative Relative Frequency Graphs

Shows the number, percentage, or proportion of observations that are
__________________ or equal to particular values.
 The number of observations falling in a given class in a frequency table,
plus all observations falling in earlier classes, divided by the total number
of observations.
 Plot a point corresponding to the to the cumulative relative frequency in
each class to the smallest value of the next class
Z-scores (Measures of Relative Standing)




Used when comparing the scores of two pieces of data that does not come from the same distribution.
Tells us how many _______________________ a particular piece of data is away from the mean of the
distribution.
Allow us to make comparisons across distributions.
A z-score is VERY useful in statistics.
If x is an observation from a distribution that has a mean μ and a standard deviation σ, then the standardize
value of x (often called the z-score) is:
𝑧=
Transforming Data
Adding the same number 𝑎 (either positive, zero, or negative) to each observation:
• __________ to measures of center and location
• ___________________ the shape of the distribution or measures of spread
Multiplying (or dividing) each observation by the same number b (positive, negative, or zero):
• ____________________ measures of center and location by _________
• ____________________ measures of spread by __________
• ________________ the shape of the distribution
Density Curves



Smooth curve that describes the overall pattern of a distribution by
showing what proportions of observations (not counts) fall into a
range of values.
Areas under a density curve represent ________________ of
observations
The total area under the curve is always equal to _______
Distinguishing Median and Mean
o The ___________of a density curve is the equal areas point.
o The ________________ of a density curve is the balance point
(like a see-saw) if the curve was made of solid material.
o The mean and the median are ____________ in a symmetric density curve.
2.2 Normal Distributions
Normal Distributions and Normal Curve



Have the same overall shape: __________________, ________________________, and
_____________________
Completely describe by giving its mean, μ, and standard deviation, σ.
Abbreviated as ________
68-95-99.7 rule
In a normal distribution with mean μ and standard deviation σ :



68% of the observations fall within __________________ of
the mean.
95% of the observations fall within __________________ of
the mean.
99.7% of the observations fall within __________________
of the mean.
The Standard Normal Distribution: The Normal
Distribution with mean 0 and standard deviation 1.

If a variable x has any Normal Distribution 𝑁(𝜇, 𝜎),
then the standard variable
𝑧=

𝑥−𝜇
𝜎
has the standard Normal Distribution
Table A is used to find the areas under the standard
Normal curve
Solving Problems Involving Normal Distributions:


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State: Express problem in terms of the observed variable, x
Plan: Draw a picture of the distribution and shade the area of intrest under the curve
Do: Perform calculations
Standardize x to restate the probloem in terms of a standard normal variable z
Use Table A to find the required area under the Standard Normal Curve
Conclude: Write your conclusion in the context of the problem.
Assessing Normality: three different methods

Construct a histogram, stem and leaf plot or box plot to determine if the shape is approximately bell
shaped with ______________________________

Check the _____________________________ (on TI-83). You are shooting for a normal probability
plot that has a linear trend to it. (quick and easy)

You can improve upon the accuracy of methods 1 and 2 by checking to see if the __________________
applies (approximately) to the data. (most time consuming)