1. Thursday, May 12, 2016 Report at 11:30 to Prairieview
AP Exam
Thursday, May 12, 2016
Report at 11:30 to Prairieview

2. Exploring Data: Describing Patterns and Departures from Patterns
We started by describing univariate (that means one variable) data graphically and numerically. Graphically:
Dotplot
Stemplot

3. More graphs… Cumulative Frequency Histogram
Will need to read, interpret and answer questions of graphs.

4. SOCS
When asked to describe data based on the graph, focus on SOCS Shape: Mound, Skewed (left or right? positive or negative?), Bimodal, Unimodal, Uniform, approximately normal… Outliers: Are there any potential? If you are only asked to describe the graph, you don’t need to calculate, just mention any potential outliers Center: Where (approx) is the median? the mean? based on the shape of the data, which is a better choice for center? Spread: Range, IQR

5. While a plot provides a nice visual description of a dataset, we often want a more detailed numeric summary of the center and spread.

6. Describing Center
Mean
Median or Q2

7. Measures of Variability: When describing the “spread” of a set of data, we can use:
Range: Max-Min
InterQuartile Range: IQR=Q3-Q1
Standard Deviation:

8. Analyzing Categorical Data
Use a bar graph to display
categorical data. Make sure graph
is labeled, bars are equal width
and evenly spaced.
A pie chart may be used
to display categorical
data if the data is parts
of a whole.

9. Conditional Distribution
Describes the values of a variable among
individuals who have a specific value of
another variable.

10. Normal Distribution
Many distributions of data and many statistical applications can be described by an approximately normal distribution.
Symmetric, Bell-shaped Curve
Centered at Mean μ
Described as N(μ, )
Empirical Rule:
68% of data within 1 of µ
95% within of µ
99.7% within 3 of µ

11. Standardizing Data
If the data does not fall exactly 1, 2, or from µ, we can standardize the value using a z-score:
You can find the or percentile by finding the area left of the z-score.
The area under a distribution curve = 1
Use table A to find percentiles or p-values
To Get area above: To Get area below:
normalcdf(z, 100, 0, 1) normalcdf(-100, z, 0, 1)
Betweeen: normalcdf (z, z, 0, 1 )

12. Assessing Normality Shape
Normal Probability Plot – Linear Plot = Normal
distribution

13. Bivariate Data (That means 2 variables)
The study of bivariate data is the study
of the relationship between quantitative
variables.
• D O F S (Direction, Outliers, Form,
Strength)
• Least Squares Regression Line
• Residuals (observed – predicted)
• Correlation (r) –Correlation Coefficient
• r2 – Coefficient of Determination
Calculator Steps:
Make sure Diagnostics are on
Enter data in L1, L2
STAT CALC LinReg (a + bx)

14. Correlation “r” We can describe the strength of a
linear relationship with the
Correlation Coefficient, r
-1 < r < 1
The closer r is to 1 or -1, the stronger
the linear relationship between
x and y.
r alone is not enough to say there
is a linear relationship between 2
variables.

15. Least Squares Regression Line
When we observe a linear relationship between x and y, we often
want to describe it with a “line of best fit” y=a+bx.
We can find this line by performing least-squares regression.
We can use the resulting equation to predict y-values for given x- values.

16. Assessing Fit
If we hope to make useful predictions of y we must assess whether
or not the LSRL is indeed the best fit. If not, we may need to find
a different model.
Use the residual plot to help determine linearity.
Plots should be scattered with no obvious
patterns or curvature.

17. Making Predictions
If you are satisfied that the LSRL provides an appropriate model for predictions, you can use it to predict a y-hat for x’s within the observed range of x- values.
Predictions for observed x-values can be assessed by noting the residual. Residual =

18. Bivariate Relationship – Non Linear
If data is not best described by a LSRL, we may be able to find a
Power or Exponential model that can be used for more accurate
predictions.
If (x,y) is non-linear, we can transform it to try to achieve a
linear relationship.
Power Model (ln x , ln y ) or ( log x , log y )
Exponential Model ( x , ln y ) or ( x , log y )
If transformed data appears linear, we can find a LSRL and then
transform back to the original terms of the data

19. Sampling and Surveys
Our goal in statistics is often to answer a question about a population using information from a sample.
Observational Study vs. Experiment
We must be sure the sample is representative of the
population in question.

20. Observational Studies
If you are performing an observational study, your
sample can be obtained in a number of ways:
Convenience
Cluster
Systematic
Simple Random Sample
Stratified Random Sample

21. Experimental Study
In an experiment, we impose a treatment with the hopes of establishing a causal relationship.
Experiments exhibit 3 Principles:
Randomization
Control
Replication

22. Experimental Designs
Like Observational Studies, Experiments can take a number of different forms:
Completely Controlled Randomized
Comparative Experiment
Blocked
Matched Pairs

23. Scope of Inference