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Histograms

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Histogram of Just the Women

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Histograms with Equal Bin Widths

bins

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Birthweights of 1230 Male Babies

50 100 150 2000

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60100 bins

50 100 150 2000

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10050 bins

50 100 150 2000

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20020 bins

50 100 150 2000

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7005 bins

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Babies of Smokers and Nonsmokers:Histograms of Weights

40 60 80 100 120 140 160 1800

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200nonsmokers

40 60 80 100 120 140 160 1800

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120smokers

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Comparison of Gestation Ages

150 180 210 240 270 300 330 3600

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gestation of non-smokers

150 180 210 240 270 300 330 3600

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gestation of smokers

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name m f r type calories protein fat sodium f iber carbo sugars potass vitami shelf weight cups rating100%_Bran N C 7 0 4 1 1 3 0 1 0 5 6 2 8 0 2 5 3 1 0.33 68.402973100%_Natura Q C 1 2 0 3 5 1 5 2 8 8 1 3 5 0 3 1 1 33.983679Al l -Bran K C 7 0 4 1 2 6 0 9 7 5 3 2 0 2 5 3 1 0.33 59.425505All-Bran_with K C 5 0 4 0 1 4 0 1 4 8 0 3 3 0 2 5 3 1 0.5 93.704912Almond_DelighR C 1 1 0 2 2 2 0 0 1 1 4 8 - 1 2 5 3 1 0.75 34.384843Apple_CinnamoG C 1 1 0 2 2 1 8 0 1.5 10.5 1 0 7 0 2 5 1 1 0.75 29.509541Apple_Jacks K C 1 1 0 2 0 1 2 5 1 1 1 1 4 3 0 2 5 2 1 1 33.174094Basic_4 G C 1 3 0 3 2 2 1 0 2 1 8 8 1 0 0 2 5 3 1.33 0.75 37.038562Bran_Chex R C 9 0 2 1 2 0 0 4 1 5 6 1 2 5 2 5 1 1 0.67 49.120253Bran_Flakes P C 9 0 3 0 2 1 0 5 1 3 5 1 9 0 2 5 3 1 0.67 53.313813Cap'n'Crunch Q C 1 2 0 1 2 2 2 0 0 1 2 1 2 3 5 2 5 2 1 0.75 18.042851Cheerios G C 1 1 0 6 2 2 9 0 2 1 7 1 1 0 5 2 5 1 1 1.25 50.764999Cinnamon_Toa G C 1 2 0 1 3 2 1 0 0 1 3 9 4 5 2 5 2 1 0.75 19.823573Clusters G C 1 1 0 3 2 1 4 0 2 1 3 7 1 0 5 2 5 3 1 0.5 40.400208Cocoa_Puffs G C 1 1 0 1 1 1 8 0 0 1 2 1 3 5 5 2 5 2 1 1 22.736446Corn_Chex R C 1 1 0 2 0 2 8 0 0 2 2 3 2 5 2 5 1 1 1 41.445019Corn_Flakes K C 1 0 0 2 0 2 9 0 1 2 1 2 3 5 2 5 1 1 1 45.863324Corn_Pops K C 1 1 0 1 0 9 0 1 1 3 1 2 2 0 2 5 2 1 1 35.782791Count_Chocula G C 1 1 0 1 1 1 8 0 0 1 2 1 3 6 5 2 5 2 1 1 22.396513Cracklin'_Oat_K C 1 1 0 3 3 1 4 0 4 1 0 7 1 6 0 2 5 3 1 0.5 40.448772Cream_of_Wh N H 1 0 0 3 0 8 0 1 2 1 0 - 1 0 2 1 1 64.533816Crispix K C 1 1 0 2 0 2 2 0 1 2 1 3 3 0 2 5 3 1 1 46.895644Crispy_Wheat_G C 1 0 0 2 1 1 4 0 2 1 1 1 0 1 2 0 2 5 3 1 0.75 36.176196

Contents of 77 Breakfast Cereals

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Histograms

50 100 150 2000

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calories0 5 10 15

0

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grams of fiber

0 5 10 150

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4

6

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12

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grams of sugars0 5 10 15 20 25

0

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15

grams complex carbohydrates

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The Vertical Axis of a Histogram

• Previous examples used counts in each bin, which is common. Comparisons are then difficult

• Book: area under histogram = 100%• Another alternative: area = 1

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Constructing a 100% Area Histogram

• Calculate percentage in each bin (“class interval”)

• Divide each percentage by the bin width, giving the height of the bar (“block”) over that bin

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Reported minus Actual GPA

What’s wrong with this histogram?

Class Interval Percent

-2.0 -- -.4 2.3

-.4 -- -.2 5.5

-.2 -- -.1 9.7

-.1 -- 0.0 21.0

0.0 -- .1 18.9

.1 -- .2 13.9

.2 -- .4 11.6

.4 -- .2 17.1

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Interval Percent W idth Density

-2.0 -- -.4 2.3 1.6 1.4

-.4 -- -.2 5.5 .2 27.5

-.2 -- .1 9.7 .1 97.0

-.1 -- 0.0 21.0 .1 210.0

0.0 -- .1 18.9 .1 189.0

.1 -- .2 13.9 .1 139.0

.2 -- .4 11.6 .2 58.0

.4 -- 2.0 17.1 1.6 10.7

Density = Percent

Width

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Bar Graphs:

Which face is happier?

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How to Lie with a Bar Graph