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INRO TO STATS

Learn tips from peers in AP Stats! Understand distributions, variables, graphs, and more. Join the quiz session for syllabus details.

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INRO TO STATS

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  1. INRO TO STATS • Sometimes the most helpful hints toward being successful in a class does not come from the teacher. • Please pass letters around the classroom and read some tips from your peers that had AP Stats just last semester in the Fall.

  2. Go to quizzizz.com/join Quiz code is on the board. It is not for a grade just to force you to look over the syllabus and expectations while I pass out books. Reference my webpage and classroom!

  3. Class Designations Class Speaker: Student who will speak to me for the class as a whole. Class Scribe: Student who does homework consistently and will write classes questions on the board daily. Class Secretary: Student with excellent note taking ability who would be willing to share notes with people who are absent.

  4. AP Statistics Section 1.1 Displaying Distributions with Graphs

  5. Distributions • A distribution can be a table or a graph. It tells us all the values a variable can take, and how often it takes those values. • Think about how data is “distributed”.

  6. Examples of Distributions

  7. Let’s start with a little vocab! • Individuals: People, animals, or things for which you are collecting data. • Variables: The values of data you are collecting (ex. How many miles a person travels in a week). Always be specific.

  8. Categorical vs. Quantitative Variables • Categorical variable – records in which category or group an individual belongs • Examples: marital status, sex, birth month, Likert scale • Quantitative variable – takes numerical values for which arithmetic operations make sense • Examples: height, IQ, # of siblings

  9. Categorical or Quantitative?

  10. Why it’s important to know the difference between categorical and quantitative variables • You will receive NO credit (really!) on the AP exam if you construct a graph that isn’t appropriate for that type of data

  11. Types of Graphs for Categorical Variables • Pie Chart • Bar Graph • Note: The bars should not “touch” each other. Bars are labeled with the category name.

  12. Pie Chart (Categorical) • Categories must make up a whole. • Percents must add up to 100%. Music preferences in young adults 14 to 19.

  13. Bar Graph (Categorical) • Represent a count OR percent. • These do not have to be part of a whole or add up to 100%.

  14. Types of Graphs for Quantitative Variables • Dotplots—place a dot above each value of the variable for every time it occurs in the data set

  15. Types of Graphs for Quantitative Variables • Stemplots – divide the data into “stems” and “leaves.” • Leaves include the last digit (you can round if necessary) • It is imperative you have a key.

  16. How to interpret graphs • Remember SOCS: Spread, outliers, center, shape • Spread—stating the smallest and largest values (note: different from the range where you actually subtract the values). We will talk about other measures of spread later. • Outliers—values that differ from the overall pattern. • Center—the value that separates the observations so that about half take larger values and about half take smaller values (in the past, you may have heard this called median). • Shape—symmetric, skewed left, skewed right. We’ll learn more about shape later.

  17. Activity • QUIETLY take your pulse for 60 seconds. Write it down on an index card. Do not put your name on the index card. Bring your index card to me.

  18. Finish up the activity • Is this data quantitative or categorical? • How could we represent this data? • Construct an appropriate graph with your group members.

  19. One-Variable Quantitative Data • The most common graph is a histogram. • It is useful for large data sets. • NOTE—histograms are appropriate graphs for one-variablequantitativedata!!!

  20. The height of each bar tells how many students fall into that class. Note that the axes are labeled! Bars include the starting value but not the ending value. The bars have equal width!!!

  21. Reading a Histogram • There are 3 trees with heights between 60 and 64. • How many trees have heights between 70 and 79? From 70 to 80? • Each value on the scale of the histogram is the START of the next bar.

  22. Shape • Symmetric – the right and left sides of the histogram are approximately mirror images of each other • Skewed Left – there is a long tail to the left • Skewed Right – there is a long tail to the right

  23. Examples of Shape Skewed left!

  24. Skewed right!

  25. Now what? • Constructing the graph is a “minor” step. The most important skill is being able to interpret the histogram. • Remember SOCS? • Spread • Outliers • Center • Shape

  26. SOCS Spread: from 7 to 22 Outliers: there do not appear to be any outliers. Center: around 15 or 16 Shape: skewed left

  27. Homework Chapter 1 #9, 16, 18, 27, 38

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