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. The following data represents the sodium content of chocolate pudding made from instant mix: 3099 3112 2401 2824 2682

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.

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?

Transforming Data

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.

What effect does adding have on the data?

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).

What if I multiplied everything by 10? Original Data

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.

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?

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

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.

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

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

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.

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

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

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

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.

Create a Modified Boxplot 56 54 75 64 76 22 81 78 66 87 62 80 68 72 59 45

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

Homework Worksheet