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Boxplots

Boxplots. Using the calculator to find mean, median, standard deviation, quartiles…. Put the data in L1 Press STAT – Calc – #1 One Var Stat. Use the calculator to find mean, median, standard deviation and interquartile range.

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Boxplots

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  1. Boxplots

  2. Using the calculator to find mean, median, standard deviation, quartiles…. • Put the data in L1 • Press STAT – Calc – • #1 One Var Stat

  3. Use the calculator to find mean, median, standard deviation and interquartile range. The following data represents the sodium content of chocolate pudding made from instant mix: 3099 3112 2401 2824 2682

  4. In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard. The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award and being unreasonable compensation. In making this determination, the court identified a “normative” group of 15 similar cases and specified a reasonable award as within 2 standard deviations of the mean of the awards in the 15 cases. What is the maximum amount that could be awarded under the “2-standard deviations rule? The following are the amount award in thousand of dollars.

  5. Gross Product 2001(in billions of dollars) • What percent are within one deviation of the mean? • What percent are within two deviations of the mean?

  6. Transforming Data

  7. Transforming Data • Transforming converts the original observations from the original units of measurements to another scale. • Transformations can affect the shape, center, and spread of a distribution.

  8. What effect does adding have on the data?

  9. Effect of Adding (or Subtracting) a Constant • Adding the same number a (either positive, zeros, or negative) to each observation • Adds a to measures of center & position(mean, median, percentiles, but • Does not change the shape of the distribution or measures of spread (range, IQR, standard deviation).

  10. What if I multiplied everything by 10? Original Data

  11. Effect of Multiplying (or Dividing) by a Constant) • Multiplying (or dividing) each observation by the same number b (positive, negative, or zero). • Multiplies measures of center and location (mean, median, quartiles, percentiles) by b • Multiplies measures of spread (range, IQR, Standard deviation) by |b|, but • Does not change the shape of the distribution.

  12. Original data has a mean of 50 and standard deviation of 5…. • What happens to both if we add 20 to each item? • What happen to both is we multiply 20 to each item? • What if we add 10 and multiply by 2?

  13. Boxplots • Provides information about the center, spread, and symmetry (skewness) of the data. • Multiple boxplots can be used to compare data.

  14. Constructing a boxplot. • Find the five number salary • Minimum • Q1 • Median • Q3 • Maximum • Plot on number line. • Box in the IQR and draw whiskers to the min & max.

  15. 5, 8, 13, 17, 22, 24, 25, 27, 29, 30

  16. 8, 10, 22, 24, 25, 25, 26, 27, 45, 72 • Graph & Describe

  17. Outlier • A value is considered an outlier if it is more than 1.5 IQR away from the closest end of the box. • It it is more than 3 IQR away from the closest end of the box then it is called an extreme outlier.

  18. 5, 7, 9, 9, 10, 11, 13, 17, 29 • Find if there are any outliers.

  19. Using the Calculator. • Put data in List • Press 2nd stat • Turn plot 1 on and choose boxplot • Zoom 9

  20. 22, 27, 33, 39, 57, 88, 110

  21. Modified Boxplot • Mild outliers are represented by shaded circles. • Extreme outliers are represented by open circles • Whiskers are only extended to largest values that are not outliers.

  22. Create a Modified Boxplot

  23. Comparative • Measure your longest finger. • Create boxplot of girls vs boys. • Describe

  24. Homework • Worksheet

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