CBSE Class 11 Economics Correlation Assignment

Points to Remember

* Meaning of correlation :

Correlatin is a statistical tool which studies the relationship between two variables. For e.g. change in price leads to change in quantity demanded.

* Correlation studies and measures the direction and intensity of relationship among variables. It measures covariation not causation.

* Types of Correlation

Correlation is classified into positive and negative correlation. 

The correlation is said to be positive when the variables move together in the same direction. For e.g. sale of Ice cream and temperature move in same direction.

The correlation is said to be negative when the variables move in opposite direction. For e.g. When you spend more time in studying chances of your failing decline.

* Examples of positive correlation are :

1. Price of commodity and amount of supply

2. Increase in height and weight.

3. Age of husband and age of wife.

4. The family income and expenditure on luxury items.

Examples of negative correlation are :

1. Sale of woollen garments and day temperature.

2. Demand of a commodity may go down as a result of rise in prices.

3. Yield of crops and price.

* Degree of Correlation :

* Methods of estimating correlation.

(a) Scatter diagram

(b) Karl pearson’s coefficient of correlation.

(c) Spearman’s rank correlation.

-- Scatter diagram offers a graphic expression of the direction and degree of correlation.

-- Karl pearson’s coefficient of correlation is a quantitative method of calculating correlation. It gives a precise numerical value of the
degree of linear relationship between two variables.

-- Karl pearson’s coefficient of correlation is also known as product moment correlation.

Here,
r = Coefficient of correlation
x = (X - X)
y = (Y - Y)
σx = Standard deviation of
X - series
σy = Standard deviation of
Y- Series
N = Number of observations

Karl pearson’s coefficient of correlation is calculated by following methods : 

Here,
∑dx = Deviations of x- series from assumed mean = (X-A)
∑dy = Deviation of Y- series from assumed mean = (Y-A)
∑dx.dy = Sum of the multiple of dx and dy
∑dx² = Sum of the square of dx
∑dy² = Sum of the square of dy
∑dx = Sum of the deviation of x- series
∑dy = Sum of the deviation of Y-series
N = Number of pairs of observations

(c) Step deviation method : 

C₁ is common factor for series - x
C₂ is common factor for series - y

* Properties of correctation coefficient (r)
(i) Correlation coefficient (r) has no unit
(ii) A negative value of r indicates an inverse relation.
(iii) If r is positive then two variables move in the same direction.
(iv) The value of r lies between minus one (1) and plus one,
-1 ≤ r ≤ 1
(v) If r is zero, the two variables are uncorrelated.
(vi) If r = +1 or r= -1, the correlation is perfect.
(viii) A high value of r indicates strong linear relationship and a low value or r indicates a weak linear relationship.
(viii) The value of r is unaffected by the change of origin and change of scale.
Given two variables x and y let us define two new variables
U = X - A/B ; V = Y - C/D
Here A and C are assumed means of X and Y respectively. B and D are common factors. They r_xy = r_uv

-Spearman’s rank correlation method is used to calculate coefficient of correlation of qualitative variables such as beauty, bravery, wisdom, ability, virtue etc. 

VERY SHORT ANSWER TYPE QUESTIONS

Question. What is meant by correlation?
Answer: Correlation is a statistical tool which studies the relationship between two variables.

Question. List some variables where accurate measurement is difficult.
Answer: Beauty, bravery, wisdom, ability etc.

Question. What is negative correlation?
Answer: The correlation is said to be negative when the variables move in opposite direction.

Question. Give the meaning of positive correlation.
Answer: The correlation is said to be positive when the variables move together in the same direction.

Question. What is the range of simple correlation coefficient?
Answer: - 1 ≤ r ≤ 1

Question. State the type of correlation when two variables change in the same ratio.
Answer: Perfect correlation.

Question. Give two examples of positive correlation?
Answer: (i) Age of husband and age of wife.
(ii) Increase in height and weight.

Question. Mention the principal short coming of scatter diagram as a method of estimating correlation.
Answer: Scatter diagram does not indicate the exact numerical value of correlation.

Question. Give two examples of negative correlation.
Answer: (i) Sale of wollen garments and day temperature.
(ii) Yield of crops and price.

Question. When is rank correlation method used?
Answer: When data are of qualitative nature like beauty, honesty etc.

Question. Mention the names of different methods for measuring correlation.
Answer: (i) Scatter diagram
(ii) Karl pearson’s coefficient of correlation.
(iii) Spearman’s Rank correlation.

Question. What is the main demerit of spearman’s rank method?
Answer: This method can not be employed for finding out correlation in a grouped frequency distribution.

Question. Mention the principal short coming of Karl Pearson’s coefficient of correlation.
Answer: The value of the coefficient is affected by extreme items.

Question. If r_xy = 0, then the variables x and y are
(i) Linearly related
(ii) not linearly related
(iii) Independent
Answer: Independent

Question. The unit of correlation coefficient between height in feet and weight in kilograms is
(i) kg / feet
(ii) percentage
(iii) non- existent
Answer: Non - existent

Question. Which method of measuring correlation measures any type of relationship?
Answer: Karl Pearson’s coefficient of correlation.