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Correlation – Class 11 Economics notes, important questions and MCQs

NCERT Class 11 Economics, chapter 6. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Correlation measures the direction and degree of the relationship between two variables. When two variables move in the same direction the correlation is positive; when they move in opposite directions it is negative. Scatter diagrams, Karl Pearson's coefficient and Spearman's rank correlation are used to study correlation. Correlation does not by itself prove cause and effect.

Types of correlation

Positive correlation: both variables move in the same direction, such as income and consumption.
Negative correlation: variables move in opposite directions, such as price and quantity demanded.
Zero correlation: no relationship, such as shoe size and marks.

Measuring correlation

A scatter diagram plots pairs of values as points; their pattern shows the type of correlation.
Karl Pearson's coefficient of correlation (r) lies between −1 and +1; r = +1 is perfect positive and r = −1 is perfect negative correlation.
Spearman's rank correlation rs = 1 − 6ΣD² ÷ (n³ − n) is used for ranks or qualitative data such as beauty or honesty.

Interpreting correlation

A high value of r shows a strong linear relationship, but not necessarily causation.
Two variables may be correlated because both depend on a third factor.
Correlation that arises purely by chance is called spurious correlation.

Key terms

Correlation: a statistical measure of the relationship between two variables
Positive correlation: a relationship in which both variables increase or decrease together
Scatter diagram: a graph of pairs of values plotted as points to show their relationship
Coefficient of correlation: a number between −1 and +1 that measures the degree of linear relationship
Rank correlation: correlation measured using the ranks of observations instead of their values

Important questions with answers

What is a scatter diagram?2 marks

A scatter diagram is a graph in which pairs of values of two variables are plotted as points. If the points rise from left to right, correlation is positive; if they fall, it is negative; if they are spread without a pattern, there is no correlation.

Why does correlation not imply causation?3 marks

Two variables may move together because both are influenced by a third factor, or purely by chance, without one causing the other. For example, ice-cream sales and drowning cases both rise in summer because of hot weather. So correlation shows only association, and causation must be established by economic reasoning.

Explain the meaning and types of correlation and the methods of measuring it.5 marks

Correlation is a statistical measure of the direction and degree of relationship between two variables. When both variables move in the same direction, as income and consumption, correlation is positive; when they move in opposite directions, as price and quantity demanded, it is negative; when there is no relationship, it is zero. It may also be perfect, high, moderate or low. Three methods are commonly used. A scatter diagram plots pairs of values as points; the pattern shows the direction and roughly the strength of the relationship, but it gives no exact value. Karl Pearson's coefficient of correlation (r) gives an exact numerical value between −1 and +1, where +1 means perfect positive, −1 perfect negative and 0 no linear correlation. Spearman's rank correlation coefficient, rs = 1 − 6ΣD² ÷ (n³ − n), uses ranks and is useful for qualitative characteristics such as beauty or intelligence, or when values are not exactly measurable. While interpreting correlation, it must be remembered that it measures only linear association and does not prove cause and effect, because variables may be related through a third factor or by chance.

Quick revision

Positive, negative, zero correlation.
Scatter diagram shows direction visually.
Karl Pearson's r between −1 and +1.
Correlation is not causation.

Exam tips

Remember the range of r: −1 ≤ r ≤ +1.
Practise Spearman's formula with a small table of ranks and D².

Practice MCQs

When two variables move in the same direction, correlation is
1. negative
2. positive
3. zero
4. spurious only
Show answer
Answer: (b) positive. Example: income and spending.
Price and quantity demanded usually have
1. positive correlation
2. negative correlation
3. zero correlation
4. perfect positive correlation
Show answer
Answer: (b) negative correlation. Price up, demand down.
The value of Karl Pearson's coefficient lies between
1. −1 and +1
2. 0 and 1
3. −10 and +10
4. 0 and 100
Show answer
Answer: (a) −1 and +1. Values outside this range indicate an error.
r = −1 means
1. no correlation
2. perfect negative correlation
3. perfect positive correlation
4. weak correlation
Show answer
Answer: (b) perfect negative correlation. Points lie on a falling straight line.
Rank correlation was developed by
1. Karl Pearson
2. Laspeyres
3. Spearman
4. Paasche
Show answer
Answer: (c) Spearman. It uses ranks.
Which tool shows correlation visually
1. index number
2. pie diagram
3. scatter diagram
4. ogive
Show answer
Answer: (c) scatter diagram. Points show the pattern.
In Spearman's formula, if ΣD² = 0 for 5 pairs, the rank correlation is
1. +1
2. 0
3. −1
4. 5
Show answer
Answer: (a) +1. 1 − 0 = 1, ranks match exactly.
Ice-cream sales and drowning cases both rise in summer. This shows that
1. ice-cream causes drowning
2. the data are wrong
3. there is zero correlation
4. correlation does not prove causation
Show answer
Answer: (d) correlation does not prove causation. A third factor, hot weather, affects both.

All chapters of Class 11 Economics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.