# Section 1-3 - PowerPoint PPT Presentation

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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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#### Presentation Transcript

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

Data

Quantitative

Qualitative

Continuous

Discrete

### 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…

• 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

### 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

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

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

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

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.