More on Histograms

Density Histograms

Density =

This ensures that the area of the rectangle is

proportional to the corresponding frequency.

Make a Density Histogram

Class Freq Rel.Freq. Density

0 - 0.1 4

0.1 - 0.2 8

0.2 - 0.4 10

0.4 - 2.0 12

L1

Freq

L3

Width

4 0.11765 0.1 1.1765

8 0.23529 0.1 2.3529

10 0.29412 0.2 1.4706

12 0.35294 1.6 0.22059

Use you

GDC to

help!

Make the

Density

Histogram

Class Interval Density

0 – 0.1 1.18

0.1 – 0.2 2.35

0.2 – 0.4 1.47

0.4 – 2.0 0.221

Density

Class Interval

Class Freq Rel. Freq. Density

0 - 10 6

10 - 20 12

20 - 40 20

40 - 60 18

60 - 100 14

Class Freq Rel. Freq. Density

0 - 10 6 0.00857

10 - 20 12 0.01714

20 - 40 20 0.01429

40 - 60 18 0.01286

60 - 100 14 0.005

Class Freq Rel. Freq. Density

0 -100 24

100 - 300 28

300 - 600 30

600 - 1000 26

Class Freq Rel. Freq. Density

0 -100 24 0.22222 0.00222

100 - 300 28 0.25926 0.0013

300 - 600 30 0.27778 0.00093

600 - 1000 26 0.24074 0.0006

Graph the following:

Interval frequency

20 – 40 35

40 – 60 27

60 – 100 20

100 - 200 10

200 – 800 28

Interval Density

20 – 40 0.01458

40 – 60 0.01125

60 – 100 0.00417

100 - 200 0.00083

200 - 800 0.00039

Bivariate

Ojive – Cumulative Frequency

Graph 1. Find the cumulative frequencies

2. Plot beginning of class on the horizontal axis and

the cumulative frequencies on the vertical axis.

Ages Frequency

13 - 19 5

19 - 25 8

25 - 31 11

31 - 37 20

37 - 43 6

Time Series – Line plot that plots each

observation against the time of the observation.

Year Life

Expectancy

1900 48.3

1910 58.1

1920 54.6

1930 61.6

1940 65.2

1950 71.1

1960 73.1

1970 74.7

1980 77.5

1990 78.8

2000 79.5

Ex: Construct a Time Series Graph

A transit manager

wishes to use the

following data for a

presentation showing

how Port Authority

Transit ridership has

changed over the years.

Year Ridership (in millions)

1990 88

1991 85

1992 76

1993 77

1994 75

Time Series Graph

65

70

75

80

85

90

1990 1991 1992 1993 1994

Freq

Year Ridership (in millions)

1990 88

1991 85

1992 76

1993 77

1994 75

Scatter plots

Graphs an ordered pair.

Put the data in L1 and L2

Press 2nd Stat Plot to turn the graph on

Press ZOOM 9 to graph

Create a scatterplot.

Wt Cl

(kg)

Total

Lifted

(kg)

46 140

50 127

54 165

59 167

64 192

70 185

76 198

83 200

Find the Line of Best Fit

Wt Cl

(kg)

Total

Lifted

(kg)

46 140

50 127

54 165

59 167

64 192

70 185

76 198

83 200 y= 1.89x + 53.0

Let’s try another one! Use it to

predict the sodium for 40 g of fat.

Fat (g) Sodium

19 920

31 1500

34 1310

35 860

39 1180

39 940

43 1260

y = 6.08x + 930

Prediction:

y = 6.08(40) + 930

y = 1173.20

Homework

Worksheet