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Concept of Variable

4.3 Concept of Variable — Understand what a variable is, how it differs from an attribute, and explore discrete vs continuous variables with examples. CBSE Class 11 Statistics notes.

Notes

Concept of Variable

Class 11 Statistics — Variable, Attribute, Discrete vs Continuous

What is a Variable?

Variable
A variable refers to a quantity or characteristic whose value varies from one investigation to another. The difference in value may be with respect to individuals, items, places or time. Each value within such range is called a ‘Variate’.

Price

Prices of different commodities are different

Age

Age of different students varies

Common Variables

Height, Weight, Wages, Expenditure, Imports, Production

Different variables are measured in different units — age in years, height in cm, income in rupees.

Think about it

Think about your class attendance register. “Age” is a variable — some students are 16, some are 17. “Height” is another variable. But “Name” is not a variable — names don’t have numerical values you can measure.

Variable vs Attribute

Variable vs Attribute
AspectVariableAttribute
NatureQuantitative characterQualitative character
MeasurabilityCan be numerically expressed (length, height, weight)Cannot be measured numerically (intelligence, beauty, efficiency)
ExamplesAge, Income, Height, ProductionLiteracy, Marital Status, Gender, Caste

Quick check

Can you measure it with a number? → Variable. Can you only describe it with words? → Attribute. “Height 165 cm” is a variable. “Tall” is an attribute.

Discrete vs Continuous Variable

Discrete Variable vs Continuous Variable
AspectDiscrete VariableContinuous Variable
MeaningTakes only exact/finite values, generally no fractional valuesCan take all possible values (integral as well as fractional) in a given range
Change in ValuesIncrease in complete numbersCan increase in fractions as well as complete numbers
Data CollectionObtained by countingObtained by measurement
ExamplesNumber of workers, students in a class, populationHeight, weight, distance, speed, temperature
Discrete can have fractions too: When there needs to be same difference between one variable and the next. Example: a coach records height in 0.5 inch increments (60.0, 60.5, 61.0…). Height is discrete here because it only takes fixed values, not every possible measurement.
Continuous Variable: A variable is said to be continuous if it is capable of passing from any given value to the next value by infinitely small measurement.

Variable Type Explorer

Discrete Variable: Takes only exact/finite values. Obtained by counting. Can only increase in complete numbers.

3 workers

Number of workers in a small shop

45 students

Students in a class (can't have 45.5)

2 cars

Vehicles a family owns

Number line:

1
2
3
4
5
…(only integer points, no fractions between)

Key Takeaways

Key Takeaways

  • A variable is a quantity whose value varies across individuals, items, or time — each specific value is called a variate.
  • Variables are quantitative (measurable); attributes are qualitative (descriptive, cannot be measured numerically).
  • Discrete variables take only exact/finite values obtained by counting (number of students, workers).
  • Continuous variables take all possible values in a range, obtained by measurement (height, weight, temperature).
  • The same characteristic can be either discrete or continuous depending on how it is recorded — a coach recording height in 0.5 inch steps makes it discrete.