Statistical Reasoning for everyday life

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Statistical Reasoningfor everyday life

• Intro to Probability and Statistics
• Mr. Spering Room 113

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3.2 Picturing Distributions of Data

• 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.
• 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)

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3.2 Picturing Distributions of Data

• (Crucial Components) Important Labels for Graphs
• 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.

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3.2 Picturing Distributions of Data

• 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.
• EXAMPLE
• Number of police officers in Crimeville, 1993 to
  2001

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3.2 Picturing Distributions of Data

• 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

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3.2 Picturing Distributions of Data

• 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.

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3.2 Picturing Distributions of Data

• 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.
• Example

Music preferences in young adults 14 to 19
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3.2 Picturing Distributions of Data

• 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.
• EXAMPLE
• Exam Scores
• of 27 students

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3.2 Picturing Distributions of Data

• 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
• Example

Data Set A   Data Set B
Leaf Stem Leaf
3 2 0 4 1 5 6 7
The numbers 40, 42, and 43 are from Data Set
A.The numbers 41, 45, 46, and 47 are from Data
Set B.
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3.2 Picturing Distributions of Data

• 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

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3.2 Picturing Distributions of Data

• 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.

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3.2 Picturing Distributions of Data

• Time-series diagram (plots over time) A
  histogram or line chart in which the horizontal
  axis represents time.
• NEXT SLIDE

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3.2 Picturing Distributions of Data EXAMPLE
Time-series diagram
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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 !!!!!!!
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3.2 Picturing Distributions of Data
How many degrees hotter was it on Wednesday than
Thursday?
30-1020 degrees hotter
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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
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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 FAVORITE INSTRUMENTS FAVORITE INSTRUMENTS FAVORITE INSTRUMENTS FAVORITE INSTRUMENTS 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?
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3.2 Picturing Distributions of Data
The following stem-and-leaf plot shows the ages
of the teachers at Central Heights Elementary
School. Which age group has the most teachers?
Stem Leaf
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
B Teachers in their thirties D Teachers in their fifties
Teachers in their thirties
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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.

1. Town A
2. Town D
3. Left out important/relevant information

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3.2 Picturing Distributions of Data

• HW pg 110 1, 5 14 all, 19, 21, 25