Percentages of State Residents in 2000 who were 65 or older

AL 13.0

AK 5.7

AZ 13.0

AR 14.0

CA 10.6

CO 9.7

CT 13.8

DE 13.0

FL 17.6

GA 9.6

HI 13.3

ID 11.3

IL 12.1

IN 12.4

IO 14.9

KS 13.3

KY 12.5

LA 11.6

ME 14.4

MD 11.3

MA 13.5

MI 12.3

MN 12.1

MS 12.1

MO 13.5

MT 13.4

NE 13.6

NV 11.0

NH 12.0

NJ 13.2

NM 11.7

NY 12.9

NC 12.0

ND 14.7

OH 13.3

OK 13.2

OR 12.8

PA 15.6

RI 14.5

SC 12.1

SD 14.3

TN 12.4

TX 9.9

UT 8.5

VT 12.7

VA 11.2

WA 11.2

WV 15.3

WI 13.1

WY 11.7

Statistics and Data Statistics and Data (Graphical)(Graphical)

Section 9.6Section 9.6

StatisticsStatisticsStatistics measures characteristics of Statistics measures characteristics of individualsindividuals(people, animals, things, etc.), called (people, animals, things, etc.), called variablesvariables; two; twovarieties:varieties:

Categorical VariableCategorical Variable – identifies individuals as – identifies individuals asbelonging to a distinct class (e.g., gender, schoolbelonging to a distinct class (e.g., gender, schoolgrade, etc.)grade, etc.)

Quantitative VariableQuantitative Variable – takes on numerical values – takes on numerical valuesfor the characteristic being measured (e.g., height,for the characteristic being measured (e.g., height,weight, etc.)weight, etc.)

Leading Causes of Death in the U.S. in 1999

Cause of Death

Heart Disease

Cancer

Stroke

Other

Number of Deaths

725,192

549,838

167,366

949,003

Percentage

30.3

23.0

7.0

39.7

What type of variables are these? Categorical!!!Categorical!!!

We can display categorical data using: bar chart,circle graph, or even a pie chart.

Leading Causes of Death in the U.S. in 1999

Causes of Death

Bar ChartBar ChartN

umbe

r of

Dea

ths

(tho

usan

ds)

200

400

600

800

1000

HeartDisease

Cancer Stroke Other

Leading Causes of Death in the U.S. in 1999

Circle GraphCircle Graph

HeartDisease30.3%

Cancer23.0%

Stroke7.0%

Other39.7%

StemplotsStemplotsStemplot (also called a stem-and-leaf plot) – aquick way to organize and analyze a small set ofquantitative data.

Each number in the data set is split into a stem,consisting of its initial digit or digits, and a leaf,which is its final digit.

Now, let’s create a stemplot fromthe “Do Now” data…

To create the stem-and-leaf plot:

1.Use the whole number part of each number as thestem, and the tenths digit as the leaf.

2. Write the stems in order down the first column and,for each number, write the leaf in the appropriate stemrow.

3. Finally, arrange the leaves in each stem row inascending order.

Stem Leaf

56789

1011121314151617

7

56 7 960 2 2 3 3 6 7 70 0 1 1 1 1 3 4 4 5 7 8 90 0 0 1 2 2 3 3 3 4 5 5 6 80 3 4 5 7 93 6

6

Notes:

• The “leafless stems”

• Spacing among the leaves

By looking at both the stemplot and the table, answer the follow-ing questions about the distribution of senior citizens among the50 states.

1. Judging from the stemplot, what was the approximate averagenational percentage of residents who were 65 or older? 12-13%

2. In how many states were more than 15% of the residents 65or older? 3 states

3. Which states were in the bottom tenth of all states in thisstatistic? Bottom 5 states in the stemplot: AK, CO, GA, TX, UT

4. The numbers 5.7 and 17.6 are so far above or below the othernumbers in this stemplot that statisticians would call them outliers.Quite often there is some special circumstance that explains thepresence of outliers. What could explain the two outliers in thisstemplot?

The average annual salaries for the top 15 U.S. metro areas areshown below. Make a stemplot that provides a good visualizationof the data. What is the average of the 15 numbers? Why is thestemplot a better summary of the data than the average?San Jose, CA 76,076San Francisco, CA 59,314New York, NY 56,377New Haven, CT 50,585Middlesex, NJ 48,977Newark, NJ 48,733Jersey City, NJ 47,514Boulder, CO 45,565Washington, D.C. 45,333Boston, MA 45,191Seattle, WA 45,171Trenton, NJ 44,576Oakland, CA 44,170Bergen, NJ 43,789Hartford, CT 42,349

Round the data to $1000 units,then create a split-stemplot :

Stem Leaf

44556677

2 4 45 5 5 5 6 8 9 916 9

6

The average annual salaries for the top 15 U.S. metro areas areshown below. Make a stemplot that provides a good visualizationof the data. What is the average of the 15 numbers? Why is thestemplot a better summary of the data than the average?San Jose, CA 76,076San Francisco, CA 59,314New York, NY 56,377New Haven, CT 50,585Middlesex, NJ 48,977Newark, NJ 48,733Jersey City, NJ 47,514Boulder, CO 45,565Washington, D.C. 45,333Boston, MA 45,191Seattle, WA 45,171Trenton, NJ 44,576Oakland, CA 44,170Bergen, NJ 43,789Hartford, CT 42,349

The average of the 15 numbersis $49,582, but this is misleading;The salaries are actually fairlytightly clustered around $45,000;The few highest salaries skewthe average upward…

Mark McGwire and Barry Bonds entered the major leagues in1986. From 1986 to 2001, they averaged 36.44 and 35.44 homeruns per year, respectively. Compare their annual home runtotals with a back-to-back stemplot. Can you tell which playerhas been more consistent as a home run hitter?

Year 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01

McGwire 3 49 32 33 39 22 42 9 9 39 52 58 70 65 32 29Bonds 16 25 24 19 33 25 34 46 37 33 42 40 37 34 49 73

Mark McGwire Barry Bonds

01234567

6 94 5 53 3 4 4 7 70 2 6 9

3

9 9 3

9 29 9 3 2 2

9 28 2

50

Which player do youthink was moreconsistent as a homerun hitter?

Frequency TablesFrequency Table for Mark McGwire’s

Yearly HR Totals

Home Runs Frequency

0 – 9

10 – 19

20 – 29

30 – 39

40 – 49

50 – 59

60 – 69

70 – 79

Total

Frequency Tables and Histograms

Frequency TablesFirst, think back to the stemplots we just completed – wheredoes the visual impact of a stemplot come from?The rows of leaves let us see how many leaves branch off each stem!!! Ex. from last class:

Mark McGwire HRs

01234567

3 9 9

2 92 2 3 9 92 92 850

The number of leaves for a particularstem is the frequency of observationswithin each stem interval.

We can also record this information ina frequency table, which gives afrequency distribution of the data.

Frequency TablesFrequency Table for Mark McGwire’s

Yearly HR Totals

Home Runs Frequency

0 – 9 3

10 – 19 0

20 – 29 2

30 – 39 5

40 – 49 2

50 – 59 2

60 – 69 1

70 – 79 1

Total 16

Notes:

• Higher frequencies in this table correspond to longer leaf rows in a stemplot.

• Unlike a stemplot, a frequency table does not display what the numbers in each interval actually are.

Histograms

HR Intervals

Histogram – gives a visual display of information from afrequency table. A histogram is to quantitative data what a barchart is to categorical data.

Fre

quen

cy

0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79

1

2

3

4

5

What are the differences betweena histogram and a bar chart?

Histogram for HR frequency of Mark McGwire

HistogramsTo create this histogram with your calculator:

• Put the lowest value of each subinterval into L (start with 0, 10, 20,…)

1

• Put the corresponding frequencies into L 2

• Settings for STAT PLOT1 – Type: Histogram (it’s a picture!), Xlist: L , Freq: L1 2

• Settings for WINDOW: Xmin = –10, Xmax = 80, Xscl = 10, Ymin = –1, Ymax = 6, Yscl = 1

NOW GRAPH!!!NOW GRAPH!!!

HistogramsNow, create a frequency table and histogram for the HR datafor Barry Bonds from last class.

Barry Bonds

01234567

6 94 5 53 3 4 4 7 70 2 6 9

3

The stemplot: Home Runs Frequency

0 – 9 0

10 – 19 2

20 – 29 3

30 – 39 6

40 – 49 4

50 – 59 0

60 – 69 0

70 – 79 1

Total 16

Frequency Table:

Histograms

HR Intervals

Fre

quen

cy

0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79

1

2

3

4

5

Histogram for HR frequency of Barry Bonds6

Make a histogram of Hank Aaron’s annual home run totalsgiven below, using interval width 5.

Year195419551956195719581959196019611962196319641965

HR132726443039403445442432

Year19661967196819691970197119721973197419751976

HR4439294438473440201210

First, create a frequency table:

HR10 – 1415 – 1920 – 2425 – 2930 – 3435 – 3940 – 4445 – 49

Total

Frequency30234362

23

Next, create the histogram(by hand and using a calculator)

Histograms

HR Intervals

Fre

quen

cy

10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49

1

2

3

4

5

Histogram for HR frequency of Hank Aaron6