Transcript 3.2 Picturing Distributions of Data

Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
3.2 Picturing Distributions of Data
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Distribution – refers to the way in which
values are spread over all possible values.
We can summarize a distribution in a table or
show a distribution visually with a graph.
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{i.e. bar graph, histogram, pareto chart, dot plot, pie
chart, stem-and-leaf plot, line chart, time-series
diagram, scatter plot, and box-whisker plot (review in
section 4.3)}
3.2 Picturing Distributions of Data
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(Crucial Components) Important Labels for Graphs
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Vertical scale – numbers along the vertical axis should clearly
indicate the scale. The numbers should line up with the tick
marks – the marks along the axis that precisely locate the
numerical values.
Horizontal scale – the categories should be clearly indicated
along the horizontal axis (Tick marks may not be necessary for
qualitative data, but should be included for quantitative data.)
Vertical axis title – Include a title that describes the variable
shown on the vertical axis
Horizontal axis title – Include a title that describes the variable
shown on the horizontal axis
Title/caption and legend (key) – the graph should have a title or
caption that explains what is being shown, and if applicable, lists
the source of the data. If multiple data sets are displayed on a
single graph, include a legend or key to identify the individual
data sets.
3.2 Picturing Distributions of Data
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Bar graph – is a diagram consisting of bars that
represent the frequencies (or relative frequencies)
for particular categories. The lengths of the bars
are proportional to the frequency.
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EXAMPLE:
Number of police officers in Crimeville, 1993 to 2001
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3.2 Picturing Distributions of Data
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Dot plot (line plot) – similar to a bar graph,
except each individual data value is represent
by a dot or symbol.
EXAMPLE:
Barley Yields, Grand Rapids
3.2 Picturing Distributions of Data
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Pareto chart – is a bar graph with the bars arranged in
order according to frequency. Pareto charts make sense
only for data at the nominal level of measurement.
3.2 Picturing Distributions of Data
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Pie Chart (circle graph) – circle divided so that
each wedge represents that relative frequency
of a particular category. The wedge size is
proportional to the relative frequency and 360
degrees. The entire pie represents the total
relative frequency of 100%.
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Example:
Music
preferences in
young adults 14
to 19
3.2 Picturing Distributions of Data
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Histogram – is a bar graph showing a distribution for
quantitative data (at the interval or ratio level); the
bars have a natural order and the bar widths have
specific meaning.
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EXAMPLE:
Exam Scores
of 27 students
3.2 Picturing Distributions of Data
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Stem-and-leaf plot – much like a histogram
turned sideways, except in place of bars we
see a listing of the individual data sources or
values. {Allows us to list all data easily}
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Example:
Data Set A
Data Set B
Leaf
Stem
320
4
Leaf
1567
The numbers 40, 42, and 43 are from Data Set A.
The numbers 41, 45, 46, and 47 are from Data Set B.
3.2 Picturing Distributions of Data
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Line chart (line graph) – shows distribution of quantitative data
as a series of dots connected by lines. Each dot is the center of
the bin it represents and the vertical position is the frequency
value for the bin. {Line charts help us to see increasing and
decreasing trends.}
 Example:
3.2 Picturing Distributions of Data
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Scatter plot – is a chart that uses Cartesian coordinates to
display values for two variables. The data is displayed as a
collection of points, each having one coordinate on the
horizontal axis and one on the vertical axis.
A scatter plot does not specify dependent or independent
variables. Either type of variable can be plotted on either axis.
Scatter plots represent the association (not causation) between
two variables.
3.2 Picturing Distributions of Data
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Time-series diagram (plots over time) –
A histogram or line chart in which the
horizontal axis represents time.
NEXT SLIDE…
3.2 Picturing Distributions of Data
EXAMPLE: Time-series diagram
3.2 Picturing Distributions of Data
Summary:
Many different ways to display data.
Remember be very observant, and study
displays carefully for misleading
information. Finally, make sure you can
recognize and interpret all forms of
display.
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3.2 Picturing Distributions of Data
GOOD LUCK !!!!!!!
3.2 Picturing Distributions of Data
DAILY HIGH TEMPERATURES
How many degrees hotter was it on
Wednesday than Thursday?
Degrees Celsius
30-10=20 degrees hotter
35
30
25
20
15
10
5
Mon. Tue. Wed. Thu. Fri.
Day
3.2 Picturing Distributions of Data
Data from an experiment was put into a circle graph and a bar graph.
Which set of bars could show the same data as the circle graph?
A
C
B
D
3.2 Picturing Distributions of Data
A band director surveyed her students to ask them their favorite
instrument. The table shows the results of the survey.
FAVORITE INSTRUMENTS
Instrument
Drums
Flute
Piano
Trumpet
Violin
Number of
Students
5
16
10
6
9
Which is the most appropriate graph of the information in the table
to show what fraction of the students choose each instrument?
FAVORITE INSTRUMENT
20
18
18
16
16
Number of Students
Number of Students
20
14
12
10
8
6
4
2
FAVORITE INSTRUMENT
Trump.
FAVORITE INSTRUMENT
Piano
14
Flute
12
10
Violin
8
Drums
6
4
xx
2
Drums Flute PianoTrump. Violin
Instrument
Drums Flute PianoTrump. Violin
Instrument
0
2
4
6
xx
8
10
x
12
14
16
18
20
22
3.2 Picturing Distributions of Data
The following stem-and-leaf plot shows the ages of the teachers at Central
Heights Elementary School.
Stem Leaf
Which age group has the most teachers?
2 4 9
3 0 3 3 7
4 1 4 5
5 2 5 8
KEY: 4 | 5 = 45
A Teachers in their twenties
C Teachers in their forties
Teachers in their thirties
B Teachers in their thirties
D Teachers in their fifties
3.2 Picturing Distributions of Data
The graph shows the population of four towns.
a.
Which town appears to have about three times the population of Town C?
b.
Which town actually has twice the population of Town C?
c.
Explain why the graph is misleading.
a. Town A
A
B
b. Town D
C
c. Left out important/relevant
information
D
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3.2 Picturing Distributions of Data
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HW: pg 110 # 1, 5 – 14 all, 19, 21, 25