copyright © 2011 pearson education, inc. statistical reasoning
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Copyright © 2011 Pearson Education, Inc.
Statistical Reasoning
Copyright © 2011 Pearson Education, Inc.
Slide 5-3
Unit 5C
Statistical Tablesand Graphs
5-C
Copyright © 2011 Pearson Education, Inc.
Slide 5-4
Frequency TablesA basic frequency table has two columns:
The first column lists the categories of data. The second column lists the frequency of each
category, which is the number of times each category appears in the data set.
Additional columns may include relative frequency (frequency expressed as a fraction or percentage of the total) or cumulative frequency (total of frequencies for the given category and all previous categories).
5-C
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Slide 5-5
Data Types and Binning
Qualitative data describe qualities or categories.
Quantitative data represent counts or measurements.
When dealing with quantitative data categories, it isoften useful to group, or bin, the data intocategories that cover a range of possible values.
5-C
Copyright © 2011 Pearson Education, Inc.
Slide 5-6
Summarizing Raw DataConsider the following 20 scores from a 100-point exam:
76 80 78 76 94 75 98 77 84 88 81 72 91 72 74 86 79 88 72 75
Determine appropriate bins and make a frequency table includingcolumns for relative and cumulative frequency.
5-C
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Slide 5-7
Bar and Pie Graphs
A bar chart shows each category with a bar whose length corresponds to its frequency or relative frequency.
Pie charts are used primarily for relative frequencies, because the total pie must always represent the total relative frequency of 100%. The size of each wedge is proportional to the relative frequency of the category it represents.
5-C
Copyright © 2011 Pearson Education, Inc.
Slide 5-8
Bar and Pie GraphsThe bar chart and pie chart below both show the data from table 5.1.
Grade Data
Grade Data
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Slide 5-9
Important Labels for Graphs
Title/caption: The graph should have a title or caption (or both) that explains what is being shown and, if applicable, lists the source of the data.
Vertical scale and title: Numbers along the vertical axis should clearly indicate the scale. The numbers should line up with the tick marks. Include a label that describes the variable.
Horizontal scale and title: 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.) Include a label that describes the variable.
Legend: 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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Copyright © 2011 Pearson Education, Inc.
Slide 5-10
Definitions A histogram is a bar graph for quantitative data
categories. The bars have a natural order and the bar widths have specific meaning.
A line chart shows the data value for each category as a dot, and the dots are connected with lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the data value for the bin.
A time-series diagram is a histogram or line chart in which the horizontal axis represents time.
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Slide 5-11
The histogram and line chart below both show the same data.
Histogram and Line Chart
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Slide 5-12
A time-series line chart of stock, bond, and gold prices for an initial $100 investment is shown below.
If you invested $100 in bonds on July 7, how much would your investment be worth on August 25?About $97.50
Reading Time-Series Diagrams
5-C
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Assignment
P. 332-335 1-24, 36, 47
Slide 5-13