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AP Stats

AP Stats. Section 1.1. Recall: Quantitative vs. Categorical Variables. Quantitative : has a numerical value that measures some characteristic of an individual. Ex: height Categorical : places each individual into a category. Ex: male or female.

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AP Stats

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  1. AP Stats Section 1.1

  2. Recall: Quantitative vs. Categorical Variables • Quantitative: has a numerical value that measures some characteristic of an individual. Ex: height • Categorical: places each individual into a category. Ex: male or female

  3. The radio audience rating service Arbitron places the country’s 13,838 radio stations into categories that describe the kind of programs they broadcast. Here is the distribution of station formats.

  4. It is always a good idea to double check your work and look for consistency. • Sometimes roundoff error occurs.

  5. Pie Chart and Bar Graph to represent the radio station data

  6. Pie Charts • Pie charts are awkward to make by hand, but software can make them for you. A pie chart must include all the categories that make up a whole. Use a pie chart only when you want to emphasize each category’s relation to the whole

  7. Bar Graphs • Bar graphs are easier to make by hand. They are also easier to read. Bar graphs can display the distribution of a categorical variable but also can compare any set of quantities that are measured in the same units.

  8. Use the bar graph on the right to answer the following: 1. Write a few sentences interpreting this graph 2. If 500 people were surveyed, how many were age 25 to 34?

  9. Stemplots • Stemplots are also known as stem and leaf plots. They show a quick picture of the shape of the data along with the actual numerical values.

  10. How to make a Stemplot?

  11. Lets make a stemplot of the following data • Look on pg 43 for data

  12. Some observations about our stemplot • The overall pattern of our stemplot is irregular, but there appear to be two clusters.

  13. Back to Back Stemplots • When you want to compare two related distributions, use back to back stemplots. • We can make a back to back stemplot comparing males and females from our original data. See next slide

  14. Males compared to Females

  15. Stemplots do not work well for large data sets where each stem must hold a large number of leaves. • Splitting Stems: Process of splitting a stem into two. One from 0 to 4 and the other 5 to 9 • Trimming: When you remove the last digit or digits before making the stemplot

  16. Histogram • A histogram breaks the range of values of a variable into classes and displays only the count or percent of the observations that fall into each class.

  17. Lets make a histogram of the following data • See pg 49 for data

  18. Some words to use • Mode: if the distribution has a peak • Symmetric: if the distribution is a mirror image on each side of the midpoint • Skewed: to the right if the right tail is much larger or vice versa

  19. Use the histogram we just made on IQ scores to describe the Shape, Center, and Spread

  20. Histograms on a Calculator • Enter Data into L1 • 2nd y= Enter • Turn on plot 1 and select the histogram type

  21. Lets construct a relative frequency and relative cumulative frequency distribution from our IQ score data • Then we will construct a relative cumulative frequency graph called an ogive

  22. Timeplot

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