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GraphsGraphs
Graphs are used to Graphs are used to present numerical present numerical information in picture information in picture form.form.
Two common types of Two common types of graphs are graphs are bar graphsbar graphs and and broken-line broken-line graphsgraphs..
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Jan. Feb. Mar. Apr. May
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Jan. Feb. Mar. Apr. May
New Car Sales
New Car Sales
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Car
sN
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ars
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Month
Components of a GraphComponents of a Graph
TitleTitle Every graph must have a titleEvery graph must have a title
SubtitlesSubtitles Explains what the horizontal and vertical Explains what the horizontal and vertical
quantities representquantities represent
Equally spaced divisionsEqually spaced divisions
ExampleExample
Looking at Looking at the graph, the graph, how many how many more cars more cars were sold in were sold in April than April than were sold in were sold in January?January?
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ars
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New Car Sales
The daily high temperatures recorded The daily high temperatures recorded during the week were as follows: Monday, during the week were as follows: Monday, 8686ºF, Tuesday, 80ºF, Wednesday, 75ºF, ºF, Tuesday, 80ºF, Wednesday, 75ºF, Thursday, 82ºF, Friday, 88ºF, Saturday, Thursday, 82ºF, Friday, 88ºF, Saturday, 74ºF, and Sunday, 84ºF. Make a bar 74ºF, and Sunday, 84ºF. Make a bar graph and a broken-line graph that present graph and a broken-line graph that present this information.this information.
Another type of Another type of graph is the pie graph is the pie graph. graph.
It is also very It is also very important to important to label to the pie label to the pie graph so that it graph so that it can be can be understood.understood.
Juan's Expenditures
$5
$10
$5
$17
$3
$2
$8 Fruit
Meats
Entertainment
Vegetables
Junk food
Breads
Dairy products
Do It Yourself!Do It Yourself! In this graph, what is the average number of In this graph, what is the average number of
type B cars sold in the 3 years shown?type B cars sold in the 3 years shown?
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Annual Car Sales
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ars
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HistogramHistogram
A histogram is A histogram is a bar graph a bar graph that shows data that shows data in groups, or in groups, or intervals. intervals.
It is often made It is often made from data from data displayed in a displayed in a frequency frequency table.table.
ScoreScore CountCount
0-90-9 11
10-1910-19 22
20-2920-29 33
30-3930-39 44
40-4940-49 55
50-5950-59 44
60-6960-69 33
70-7970-79 22
80-8980-89 22
90-9990-99 11
Frequency Table
Histogram
ExampleExample Which category represents about 30% of the Which category represents about 30% of the
total number of books?total number of books?
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68 72
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Number of Books
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Age of Books (years)
Number of Books in the School Library by Age
1-5
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11-15
Scatter Plot is a graph of two related sets Scatter Plot is a graph of two related sets of data on an XY axis.of data on an XY axis.
These are useful when you want to study These are useful when you want to study related pairs, such as height and weight.related pairs, such as height and weight.
Correlation is the relationship between two Correlation is the relationship between two or more things.or more things.
Linear correlation is a scatter plot that Linear correlation is a scatter plot that forms a “line” showing that one axis seems forms a “line” showing that one axis seems to depend on or relate to the other.to depend on or relate to the other.
Linear CorrelationsLinear Correlations
Positive linear correlation Negative linear correlationPositive linear correlation Negative linear correlation
Linear CorrelationLinear Correlation
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Constant correlation
Line of Best FitLine of Best Fit Line of best fit- Line of best fit- line that seems to describe the direction line that seems to describe the direction
the points are heading in the points are heading in
There are methods for determining where this line is, but There are methods for determining where this line is, but for our purposes we'll use just two criteria to find and for our purposes we'll use just two criteria to find and draw the line:draw the line:
- The line of best fit must more or less follow the direction - The line of best fit must more or less follow the direction of the points.of the points.- There should be roughly the same number of points on - There should be roughly the same number of points on each side of the line.each side of the line.
Lines of best fit can be used to predict results, especially Lines of best fit can be used to predict results, especially if you find the line's equation. We'll look at this in more if you find the line's equation. We'll look at this in more detail later. detail later.
Example of Line of Best FitExample of Line of Best Fit
ExampleExample To find out an approximate To find out an approximate
income for someone who income for someone who is 51 years old, we read is 51 years old, we read the value from the graph:the value from the graph:
- Find age 51 on the x-axis.- Find age 51 on the x-axis.- Draw a vertical line up to - Draw a vertical line up to the line of best fit.the line of best fit.- Draw a horizontal line - Draw a horizontal line from there, back to the y-from there, back to the y-axis. axis.
This gives us the income of This gives us the income of someone who is 51 years old someone who is 51 years old ... approximately $61,500. ... approximately $61,500.
Misleading GraphsMisleading Graphs
http://www2.fiu.edu/~graphing/mislead3.htm http://www2.fiu.edu/~graphing/mislead3.htm
http://www.northcanton.sparcc.org/http://www.northcanton.sparcc.org/~technology/excel/files/~technology/excel/files/misleading_graphs.html misleading_graphs.html
http://www.bbc.co.uk/schools/gcsebitesize/http://www.bbc.co.uk/schools/gcsebitesize/maths/data/representingdata2rev5.shtml maths/data/representingdata2rev5.shtml
