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Data Analysis Techniques in Statistics Studies

Learn about stem-and-leaf plots, pie charts, Pareto charts, and scatter plots. Understand measures of central tendency like mean, median, and mode. Calculate weighted means and explore shapes of distributions.

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Data Analysis Techniques in Statistics Studies

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  1. Section 2.2 More Graphs and Displays

  2. Stem-and-Leaf Plots • Each number is separated into a STEM and LEAF component. • The STEM is the leftmost digit(s). • The LEAF is the rightmost digit. • It’s important to include a key to identify values. For example… Key: 15 | 5 = 155

  3. Use the stem-and-leaf plot to list the actual data entries.

  4. Make a stem-and-leaf plot: • Ages of the top 30 highest paid CEOs (Forbes Magazine).

  5. Pie Chart (for Qualitative Data) • A circle divided into sectors that represent categories. • The area of each sector is proportional to the frequency of the category.

  6. Pareto Chart (for Qualitative Data) • Vertical bar graph in which the height of each bar represents the frequency or relative frequency. • Bars are positioned in order of decreasing height, left to right. • EX: Make a Pareto chart • Ultraviolet indices for 5 cities at noon:

  7. Scatter Plot (for Paired Data Sets) • Paired data  Ordered pairs. • Plot on a coordinate plane. • Independent variable on the x-axis.

  8. EX: make a scatter plot:

  9. Section 2.3 Measures of Central Tendency

  10. Measure of Central Tendency: • A value that represents a typical, or central, entry of a data set. • 3 most common are MEAN, MEDIAN, and MODE

  11. MEAN: sum of the data entries divided by n

  12. MEDIAN • The data entry in the MIDDLE. • List data from least to greatest. • Find the middle value. • (For even n, find the average of the 2 middle values)

  13. MODE • Data entry that occurs MOST often (highest frequency) • A data set may have no mode or have more than mode. • BIMODAL = 2 modes.

  14. EX: Find mean, median, and mode for the data set. • The 2012-2013 tuition and fees (in thousands of dollars) for the top 14 universities: 41 39 42 47 45 42 42 44 44 40 45 44 44 44

  15. Weighted MEAN: data values have different weights.

  16. EX: find the weighted mean • The scores and their percents of the final grade for an archaeology student are shown. What is the student’s mean score:

  17. Ex: find the weighted mean • The mean scores for students in a statistics course (by major) are shown below. What is the mean score for the class? 9 engineering majors: 85 5 math majors: 90 13 business majors: 81

  18. Mean of a Frequency Distribution

  19. EX: Find the mean • The city mileage (in miles per gallon) for 24 family sedans:

  20. Shapes of Distributions • Distributions may look .. • Symmetric • Uniform • Skewed Left • Skewed Right

  21. Symmetric

  22. Uniform

  23. Skewed Left

  24. Skewed Right

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