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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 Spread. Checking for Outliers.

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Ap review

AP Review

Exploring Data

Describing a distribution
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 Spread

Checking for outliers
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 outliers1
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 and Sensitive Statistics

  • Robust (not affected by extreme values)

    Median, IQR

  • Sensitive (affected by extreme values)

    Mean, s, range

Parameters and statistics
Parameters and Statistics

  • Parameters are numerical values that describe a population.

  • Statistics are numerical values that describe a sample.

Z scores and percentiles
Z – Scores and Percentiles

  • Barron’s p. 41 #10

  • Assuming that batting averages have a bell-shaped 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.


Normal distribution
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.

Linear regression
Linear Regression

  • 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.

Linear regression1
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 regression2
Linear Regression

  • Influential Point – pulls regression line toward it. An influential point is usually a point in the x-direction.

  • Outlier – shows up in residual plot usually in the y – direction.

Linear regression3
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
Barron’s Problems

  • Multiple Choice

    P. 370 #13, 14, 16, 19, 21, 24, 27, 30, 38

  • Free Response

    P. 430 #2