Chapter 2

Descriptive Statistics

2.2 More Graphs and Displays

Pie Chart

Pareto

Scattered Plot

Stem and Leaf

Time Series graph

Dot Plot

A Stem and Leaf plot is a way to display quantitative data.

This is a relatively new method way of displaying data.In a stem and leaf and leaf plot , each number is separated into a stem (the leftmost digit or digits) and leaf (the rightmost digits) Leaf

values

Stemvalues

192225262728293034363742

434446484849525355575862

Benefit: A stem and leaf plot is similar to a histogram except all of the original data is still there (not embedded in classes or buckets)

Example Stem and Leaf plot

In 2013 Major league first basemen hit the following number of homeruns: 25, 30, 22, 14, 15, 17, 17, 53, 36, 20, 20, 20, 44, 17, 15, 21, 36, 22, 23, 24, 23

Since the data includes 10s, 20s, 30s, 40s and 50s your stems will be1, 2, 3, 4, and 5

Step 1 : decide on the stems

12345

50

2

Data can be ordered or unordered

A dot plot is another way to display quantitative data.

Data is displayed above a horizontal axis. Each dot is a single instance of the corresponding number on the x axis

Horizontal axis should extend to cover all data, even outliersOutliers are unusual data. They don’t seem to fit in the data set

Four instances

of 25

An example of an outlier in the data set above would have been a number > 40

Example Dot Plot

In 2013 Major league first basemen hit the following number of homeruns: 25, 30, 22, 22, 15, 17, 17, 53, 36, 20, 20, 20, 44, 17, 15, 21, 36, 14, 23, 24, 23

Since the minimum number of homeruns was 14 and the max was 53 it has to be at least that long

Step 1 : decide on length of horizontal line

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

. ...

Pie charts provide a convenient way of looking at qualitative data.

A Pie Chart divided into sectors that represent the categories.

The area of each sector is proportional to the frequency of each category.

Benefit: At a quick glance you can see that most fatalities were from cars

  fRelative Frequency Angle

Cars 20,260 0.56 202o

Trucks 12,260 0.34 122o

Motorcycles 3,067 0.08 29o

Other 610 0.02 72o

56%34%

8%

2%

Motor Vehicle Occupants Killed in 2001

CarsTrucksMotorcyclesOther

Example Pie Chart

In 2008 Crisco conducted a national survey as the pie preference of Americans

The study revealed that 9% preferred Cherry, 19% Apple, 12% Pecan, 8% Lemon meringue, 13% Pumpkin, 10% Banana cream and 29% preferred some other pie.

The first step is to prepare a frequency distribution chart with relative frequencies.

 Relative frequency

Apple 0.19Pumpkin 0.13Pecan 0.12Banana cream 0.1Cherry 0.09Lemon meringue 0.08Other 0.29

The next step is to, starting at 12:00 (straight up), insert appropriately sized sectors.

Apple19%

Pumpkin13%

Pecan12%Banana cream

10%Cherry

9%

Lemon meringue

8%

Other29%

Pie preferences of Amer-icans

Another way to graph qualitative data is to use a Pareto chart

A Pareto chart is a vertical bar in which the height of each bar represents the frequency or relative frequency.

To construct you will need to construct a frequency table

Pareto graphs are the most frequently used in the business world

Domestic car sales for June 2014Vehicle Sales in thousands

Ford F series 60Chevrolet Silverado 43Toyota Camry 40Ram Pickup 33Honda Accord 32Honda Civic 32Toyota Corolla 31Ford Fusion 27Ford Focus  26Honda CRV 26

0

10

20

30

40

50

60

70

June Car Sales

Doll

ars

in

thousa

nds

Good form is to have data in descending order

Example Pareto Chart/Graph

According to Business Life the 10 richest Hollywood male actor/celebrities are: Arnold Swarzenegger($300M), Tom Hanks($350M), Jack Nicholson($385M), Merv Griffin($1000M), Shakruch Khan($600M), Michael Douglass($290M), Johnnie Depp($360M), Sylvester Stallone($430M), Tom Cruise ($400M) and Mel Gibson($640M).To make a Pareto you will need to put them and their respective earnings in a table…in descending order

Actor Dollars ($$$) in MillionsMerv Griffin 1000Mel Gibson 640Shakruk Khan 600Sylvestor Stallone 430Tom Cruise 400Jack Nicholson 385Johnnie Depp 360Tom Hanks 350Arnold S 300Michael Douglas 290

Mer

v Griffin

Mel

Gib

son

Shakr

uk K

han

Sylve

stor

Sta

llone

Tom

Cru

ise

Jack

Nic

hols

on

John

nie

Dep

p

Tom

Han

ks

Arnol

d S

Mic

hael

Dou

glas

0

400

800

1200

Richest Actors

$$$s

in M

illi

ons

When one entry in one data set corresponds to one entry in a second data set, the sets are called Paired sets.

One way to graph paired data is to use a scattered plot. A scattered plot shows the relationship between two quantitative variables.

The example below is a restaurant owner who recorded the temperature and his ice cream sales for 10 days.

Temp FoIce Cream Sales in $$$s

58 21561 32553 18559 33265 40672 52267 41277 61474 54469 42173 44563 408

77 74 73 72 69 67 65 63 61 59 58 530

100

200

300

400

500

600

700

Ice Cream Sales/ Temperature Scatter plot

Temperatur e in Farenheit

$ i

n S

ale

s

Paired sets

Example Scatter Plot and Paired Data set

A teacher asked her students to write the number of hours they had studied at the bottom of a test.

After grading she put the scores and hours studied in a paired data matrix

She then graphed the points to look for trends

She decided that the hours studied would be the y axis, and the score would be the x axis………but this was just a preference.

30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

Study vs Final Score graph

Score

Hours

stu

die

d

Score

Study Hours

50 1

40 1

75 2

65 2

80 3

90 5

80 6

90 7

85 7

100 7

A data set that is composed of quantitative entries taken at regular intervals is Time Series.

You can use a time series chart to graph a time series.

The chart below breaks time down in year and season (x axis) and production in thousands of tons (y axis).

Example Time Series

A teacher teacher assigned her students to do a time series graph for the 21st century Dow Jones highs.

The first thing the student does is make a table full of ordered pairs (years and highs) of data from the Dow Jones Industrial site.

Year Dow Jones Yearly high

2000 110002001 113002002 106002003 100002004 106002005 107002006 109002007 141002008 130002009 105002010 112002011 128002012 135002013 162002014 17000

Next, plot each ordered pair on a line graph

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Dow Jones HistoryYearl

y I

ndex H

igh

Graph the following Data. Use the appropriate graphs.

Year

Voters in 

million voters

2008 1312004 1222012 1211992 1062000 1051996 961984 931988 921980 861976 81

New Mexico

121,589 sq mi

Nevada110,560

sq mi

Texas268,580

sq mi

Oregon98,380 sq

mi

Wyoming97,813 sq

mi

Alaska663,267

sq mi

Colorado104,093

sq mi

Arizona113,998

sq mi

Montana147,042

sq mi

California163,695

sq mi