histograms - university of california, berkeleyrice/oldstat20_s98/chapt3.pdf · 1998-01-23 ·...

1

Histograms

2

Histogram of Just the Women

3

Histograms with Equal Bin Widths

bins

4

Birthweights of 1230 Male Babies

50 100 150 2000

10

20

30

40

50

60100 bins

50 100 150 2000

20

40

60

80

10050 bins

50 100 150 2000

50

100

150

20020 bins

50 100 150 2000

100

200

300

400

500

600

7005 bins

5

Babies of Smokers and Nonsmokers:Histograms of Weights

40 60 80 100 120 140 160 1800

50

100

150

200nonsmokers

40 60 80 100 120 140 160 1800

20

40

60

80

100

120smokers

6

Comparison of Gestation Ages

150 180 210 240 270 300 330 3600

50

100

150

200

250

gestation of non-smokers

150 180 210 240 270 300 330 3600

50

100

150

200

gestation of smokers

7

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

8

Histograms

50 100 150 2000

5

10

15

20

25

30

calories0 5 10 15

0

5

10

15

20

25

30

35

grams of fiber

0 5 10 150

2

4

6

8

10

12

14

grams of sugars0 5 10 15 20 25

0

5

10

15

grams complex carbohydrates

9

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

10

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

11

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

12

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

13

Bar Graphs:

Which face is happier?

14

15

How to Lie with a Bar Graph