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Introduction to Statistics. Section 1-3. Objectives. After completing this section, you should be able to: Identify types of variables Qualitative Quantitative Identify the measurement level for each variable. Classification of Data. Data. Quantitative. Qualitative. Continuous.

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Section 1-3

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Section 1 3

Introduction to Statistics

Section 1-3


Objectives

Objectives

After completing this section, you should be able to:

  • Identify types of variables

  • Qualitative

  • Quantitative

  • Identify the measurement level for each variable


Classification of data

Classification of Data

Data

Quantitative

Qualitative

Continuous

Discrete


Examples of variables

Examples of variables

  • Qualitative: variable that can be placed into distinct categories.

    Examples: gender, location, hobby

  • Quantitative: variables that are numerical and can be ordered or ranked.

    Examples: age, height, weight

    Note: discrete variables are quantitative in nature. These are variables that assume variables that can be counted.


Continue

Continue…

  • Examples of discrete variables:

    number of children in a family; number of students in a classroom; number of books in your home library.

  • Continuous variables are also quantitative in nature. These are variables that can assume an infinite number of values between any two specific values.

    Example: Height…There are infinite heights between 180 cm and 181 cm


Recorded values and boundaries

Recorded Values and Boundaries


Classification of data again

Classification of data…again

  • Recall: variables can be classified to qualitative or quantitative.

  • Variables can also be classified according to the way they are categorized, counted, or measured.

  • This type of classification uses measurement scales.

  • There are four common types: nominal, ordinal, interval, and ratio.


Nominal level of measurement

Nominal Level of Measurement

When you classify data into mutually exclusive categories in which no order or ranking can be imposed on the data.

Examples

  • A sample of teachers classified according to subject taught (e.g. math, physics, English).

  • A sample of people classified according to their marital status (single, married, divorced, widowed).


Ordinal level of measurement

Ordinal Level of Measurement

When you classify data according to categories that can be ordered or ranked; however, precise differences between the ranks do not exist.

Examples:

  • A sample of people in a company classified according to their salaries,

  • A sample of players in a football team classified according to their height (short, medium, tall)

  • A sample of students in a school classified according to their letter grades (A, B, C, D, F).


Interval level of measurement

Interval Level of Measurement

When you classify data according to categories that can be ranked or ordered and precise differences between units of measure exist; however, there is no meaningful zero. That is, there is no absolute zero.

Example:

  • A sample of people classified according to their IQ score.

    There is a meaningful difference of 1 point between an IQ of 110 and IQ of 109. However, there is no true zero. IQ tests do not measure people who have no intelligence.


Ratio level of measurement

Ratio Level of Measurement

When you classify data according to categories that can be ranked or ordered and precise differences between units of measure exist; however and there is a meaningful zero. That is, there is an absolute zero. In addition, true ratios exist when the same variable is measured on two different members of the population.

Examples:

  • Height, weight, age, number of students in a class.

  • Also, if one person can run for 6 km and another can run for 3 km, then the ratio between them is 2 to 1.In other words, the first person can run as twice as much as the second person.


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