Percentages of State Residents in 2000 who were 65 or older AL13.0 AK5.7 AZ13.0 AR14.0 CA10.6 CO9.7...
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Transcript of Percentages of State Residents in 2000 who were 65 or older AL13.0 AK5.7 AZ13.0 AR14.0 CA10.6 CO9.7...
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