Boxplots

Using the calculator to find mean, median, standard deviation,

quartiles….O Put the data in L1O Press STAT – Calc –

O #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:

30993112240128242682

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.37 75 135 140 150

238 340 600 750 7501050 1139 1200 1200 1576

Gross Product 2001(in billions of dollars)

O What percent are within one deviation of the mean?

O What percent are within two deviations of the mean?

110 24 134 62 1119 14231 426 174 85 77 10762 163 20 52 63 4182 105 364 30 100 21142 34 54 419 254 40129 32 165 239 295 161319 48 707 236 17 341160 646 60 16 231 19340 158 18

Transforming Data

Transforming DataO Transforming converts the original

observations from the original units of measurements to another scale.

O 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 ConstantO Adding the same number a (either

positive, zeros, or negative) to each observationO Adds a to measures of center &

position(mean, median, percentiles, but

O Does not change the shape of the distribution or measures of spread (range, IQR, standard deviation).

What if I multiplied everything by 10?

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2

3

4

5

Original Data

Effect of Multiplying (or Dividing) by a Constant)

OMultiplying (or dividing) each observation by the same number b (positive, negative, or zero).

O Multiplies measures of center and location (mean, median, quartiles, percentiles) by b

O Multiplies measures of spread (range, IQR, Standard deviation) by |b|, but

O Does not change the shape of the distribution.

Original data has a mean of 50 and standard

deviation of 5….O What happens to both if we add 20 to each item?

O What happen to both is we multiply 20 to each item?

O What if we add 10 and multiply by 2?

BoxplotsO Provides information about the

center, spread, and symmetry (skewness) of the data.

O Multiple boxplots can be used to compare data.

Constructing a boxplot.O Find the five number salary

O MinimumO Q1

O MedianO Q3

O MaximumO Plot on number line.O 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

O Graph & Describe

OutlierO A value is considered an outlier if it

is more than 1.5 IQR away from the closest end of the box.

O 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

O Find if there are any outliers.

Using the Calculator.O Put data in ListO Press 2nd statO Turn plot 1 on and choose boxplotO Zoom 9

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

Modified BoxplotO Mild outliers are represented by

shaded circles.O Extreme outliers are represented by

open circlesO 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

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

Homework

O Worksheet