Types of Data and Scales of Measurement

In statistics, data can be classified in different ways depending on what is being measured and how it is measured. Understanding these classifications is important for choosing the right statistical methods.

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I. Types of Data

Data can be broadly classified into Qualitative and Quantitative data.

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1. Qualitative Data (Categorical Data)

This data describes qualities, categories, or characteristics. It is non-numerical (though sometimes numbers may represent categories).

Types of Qualitative Data

a. Nominal Data

• Represents names, labels, or categories
• No natural order Examples: gender, religion, colors, blood group

b. Ordinal Data

• Represents categories with a meaningful order
• The difference between ranks is not measurable Examples: ranks (1st, 2nd, 3rd), satisfaction levels (good, average, poor)

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2. Quantitative Data (Numerical Data)

This data represents numbers and can be measured.

Types of Quantitative Data

a. Discrete Data

• Takes only specific, countable values
• Often whole numbers Examples: number of students, number of cars, goals scored

b. Continuous Data

• Can take any value within a range
• Measured, not counted Examples: height, weight, temperature, time

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II. Scales of Measurement

Introduced by S.S. Stevens, the four scales determine how data can be analyzed. From lowest to highest level of measurement:

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1. Nominal Scale

• Used for labeling categories
• No order
• Numbers have no mathematical meaning

Examples:

• 1 = Male, 2 = Female
• Types of fruits
• Blood group

Permitted Operations: counting frequencies, mode

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2. Ordinal Scale

• Categories have an order
• Exact differences between ranks are unknown

Examples:

• Grades (A, B, C)
• Ranking in a race
• Satisfaction levels

Permitted Operations: comparison (<, >), median, percentiles

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3. Interval Scale

• Numeric scale with ordered values
• Equal intervals between values
• No true zero point

Examples:

• Temperature in Celsius or Fahrenheit
• IQ scores

Permitted Operations: addition, subtraction, mean, SD No meaningful ratios (e.g., 20°C is not “twice” as hot as 10°C)

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4. Ratio Scale

• Highest level of measurement
• Has a true zero
• Ratios are meaningful

Examples:

• Height, weight
• Age
• Salary
• Distance

Permitted Operations: all mathematical operations (mean, median, mode, ratios)

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Comparison Table

Type	Characteristics	Examples
Nominal	Categories only, no order	Gender, colors
Ordinal	Ordered categories	Rank, satisfaction level
Interval	Equal intervals, no true zero	Temperature (°C, °F)
Ratio	Equal intervals + true zero	Height, weight, age

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Quick Memory Trick

• Nominal → Name
• Ordinal → Order
• Interval → Equal intervals, no real zero
• Ratio → Real zero, all math allowed

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