Discrete Graphs Andrew Samuels. Data Set – a collection of data values Data Points – individual...
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DiscreteGraphs
Andrew Samuels
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Data Set – a collection of data values
Data Points – individual values within a data
set (can consist of many numbers)
N – the size of the data set
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A professor presented his class the results of their Statistics 101 Midterm exam:
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Frequency table – gives the frequency of the occurrence
Here the professor presented the same data in a frequency table
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Bar graph – presents information from the Frequency table in a graph
Here the professor presented the same data in a Bar graph
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Outliers – extreme data points that do not fit the overall pattern of the data
Relative frequencies – frequencies given in terms of percentages of the total population
Here the professor presented the same data in a Relative frequency Bar graph
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Pictogram – Frequency charts that use icons or pictures instead
of bars
Here the professor presented the same data in a Pictogram
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Evaluate the following Pictograms that represent the same data:
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Tricks to mislead in presenting Bar graph data
1)Stretching the scale of the vertical axis
2)Cheating on the starting value on the vertical axis
Look for objectivity verse propaganda
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Variables
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Variable – any characteristic that varies with the members of a population
i.e. Scores, time spent studying
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Two Types of variables:
1.) Quantitative (numerical) variable – a variable that represents a measurable quantity.
Can be either continuous or discrete:
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Continuous – when the difference between the values of the quantitative variable can be arbitrarily small ex.) height, weight, foot size, time to run a 5k
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Discrete - when the difference between the values of the quantitative variable change by minimum increments ex.) IQ, SAT scores, shoe size, points in a game
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Sometimes the lines between continuous and discrete can become blurred like rounding weight to the nearest pound would make this discrete.
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2.) Qualitative (categorical) variables – cannot be measured numerically
Ex. Nationality, gender, hair color
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Here is data about the enrollment at the five schools at Tasmania State University. Other includes undeclared students, interdisciplinary majors, ect.
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Here are two Bar graphs showing the same data in different ways. Some prefer the later graph when presented with qualitative (categorical) variables.
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Pie chart – the entire population is the pie (100%) - each slice is proportional to the relative frequency of the corresponding category.
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360⁰/100 = 3.6⁰ x% is given by an angle measure of 3.6x degrees
Here is a Pie chart composed of data gathered by Nielsen. Prime time is 8 – 11pm
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Children make up 15% of the population at large
Teens make up 8%
Using absolute percentages can be misleading.
*When comparing characteristics of a population that is broken up into categories, it is essential to take into account the relative sizes of the various categories
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Class Intervals
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At times there may be too many categories to represent data clearly using a Bar graph or Pie chart. Such is the case with SAT scores. They range from 200 – 800 in increments of 10 points. The data presented like this would produce 61 different possible categories, too many for an effective Bar graph.
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Class Intervals – aggregating (grouping together) data points into categories.
Rule of thumb – you should have between 5 and 20 class intervals
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Class Intervals are needed to convert test scores (quantitative/numerical variable) into grades (qualitative/categorical variable).
The professor could convert using an absolute scale (like a ten or seven point system), or a relative scale (fit class intervals to class performance on that test “curve”).
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Histogram – variation of a bar graph used to display a continuous quantitative variable.
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Starting salaries of last year’s graduating class TSU
N = 3258
Salary range $40,350 - $74,800Class intervals must be set up
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Since the data is continuous, a histogram has no gaps between class intervals.
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Endpoint Convention – where does the data fall if it is exactly on the boundary between two classes?
Simple Histograms are designed with class intervals of equal length.