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A collection of methods for planning studies
and experiments, obtaining data, and then
organizing, summarizing, presenting,
analyzing, interpreting, and drawingconclusions based on the data
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A variable is a characteristic or condition
that can change or take on different values.
Most research begins with a general question
about the relationship between two variablesfor a specific group of individuals.
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The entire group of individuals is called the
population.
For example, a researcher may be interested
in the relation between class size (variable 1)and academic performance (variable 2) for
the population of third-grade children.
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Usually populations are so large that a
researcher cannot examine the entire group.
Therefore, a sample is selected to represent
the population in a research study. The goalis to use the results obtained from the
sample to help answer questions about the
population.
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Variables can be classified as discrete orcontinuous.
Discrete variables (such as class size)consist of indivisible categories, andcontinuous variables (such as time orweight) are infinitely divisible into whateverunits a researcher may choose. For example,time can be measured to the nearest minute,
second, half-second, etc.
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To define the units for a continuous
variable, a researcher must use real limits
which are boundaries located exactly half-
way between adjacent categories.
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To establish relationships between variables,researchers must observe the variables and recordtheir observations. This requires that the variablesbe measured.
The process of measuring a variable requires a setof categories called a scale of measurement and aprocess that classifies each individual into onecategory.
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1. A nominal scale is an unordered set ofcategories identified only by name.Nominal measurements only permit you todetermine whether two individuals are the
same or different.2. An ordinal scale is an ordered set of
categories. Ordinal measurements tell youthe direction of difference between two
individuals.
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3. An interval scale is an ordered series of equal-
sized categories. Interval measurements
identify the direction and magnitude of a
difference. The zero point is locatedarbitrarily on an interval scale.
4. A ratio scale is an interval scale where a value
of zero indicates none of the variable. Ratio
measurements identify the direction andmagnitude of differences and allow ratio
comparisons of measurements.
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0
2
4
6
8
10
12
14
Series 3
Series 2
Series 1
Sales
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
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observations (such as measurements,
genders, survey responses) that have been
collected
Raw data are collected data that have beenorganized numerically.
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Array
An array is an arrangement raw numerical data in
ascending or descending order of magnitude. The
difference between
Tally marks
E.g.
1 5 3 3 2
3 0 4 1 4
3 3 2 1 2
1 1 0 3 6
5 0 3 4 2
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Stem Plot E.g. 44, 46, 47, 49, 63, 64, 66, 68, 68, 72, 72, 75, 76, 81,
84, 88, 106
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Frequency Distribution
Cumulative Frequency
Class Intervals and Class LimitsClass boundaries
Size or width of a class interval
Class mark(midpoint)
Height " No. of Students
60-62 5
63-65 18
66-68 42
69-71 2772-74 8
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Histogram
Frequency Polygons
Cumulative- Frequency distributions and
Ogives
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68 84 75 82 68 90 62 88 76 93
73 79 88 73 60 93 71 59 85 75
61 65 75 87 74 62 95 78 63 72
66 78 82 75 94 77 69 74 68 60
96 78 89 61 75 95 60 79 83 71
79 62 67 97 78 85 76 65 71 75
65 80 73 57 88 78 62 76 53 74
86 67 73 81 72 63 76 75 85 77
Final grades in mathematics of 80 students at the department of
finance are given below.
1. The highest grade
2. The lowest grade
3. The range
4. The grade of the five highest ranking students5. The grade of the five lowest ranking students
6. The grade of the student ranking tenth highest
7. The No. of students who received grades of 75 or higher
8. The No. of students who received grades below 85
9. The % of students who received grades higher than 65 but not higher
than 85
10. The grades that did not appear at all
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138 164 150 132 144 125 149 157
146 158 140 147 136 148 152 144
168 126 138 176 163 119 154 165
146 173 142 147 135 153 140 135
161 145 135 142 150 156 145 128
In the following table the weights of 40 male students at the
department of Finance are recorded to the nearest pound.
1. Construct the Frequency and CF Distribution
2. Plot the data on a histogram
3. Draw the Frequency polygon
4. Draw the Ogive
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