Statistics: Basic Concepts, Data Collection and Presentation

7/29/2019 Statistics: Basic Concepts, Data Collection and Presentation

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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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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

Statistics: Basic Concepts, Data Collection and Presentation

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