Karl Pearson Method
Introduction
Correlation helps in identifying the nature, direction and degree of relationship between two variables.
The various techniques for measuring correlation are:
Scatter Diagram
Karl Pearson’s Coefficient of Correlation and
Spearman’s Rank Correlation
Scatter Diagram is a graphic method of studying correlation between two variables.
There are mainly five types of scatter diagram; positive correlation, negative correlation, perfect positive correlation, perfect negative correlation and no correlation.
The various merits of scatter diagram are; it is the most simple method of studying the relationship between the two variables, it is unaffected by extreme values, etc.
The various demerits of scatter diagram are; it does not measure the precise extent of correlation, etc.
Karl Pearson’s Coefficient of Correlation is popularly known as coefficient correlation. It is denoted by the symbol ‘r’.
The various properties of correlation coefficient are: the change of scale and origin has no effect on correlation coefficient. Correlation coefficient is independent of the unit of measurement, etc.
Methods to Calculate Karl Pearson’s Coefficient of Correlation are:
Actual Mean Method
Direct Method
Assumed Mean Method
Step Deviation Method
The various merits of Karl Pearson’s coefficient are; it is based on all observations of series, helpful in further algebraic analysis, etc. The demerits of Karl Pearson’s coefficient are; it is affected by extreme items, calculation process is time consuming, etc.
The various demerits of rank correlation are; combined ‘r’ of different series cannot be obtained, it cannot be treated for further algebraically, etc.
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Q1
Write the formula through which Coefficient of correlation can be obtained without finding out the deviations?
Marks:2Answer:
Coefficient of correlation can be obtained without finding out the deviation from mean of the series with the help of below given formula:

Q2
Calculate the correlation coefficient:
Squared deviation from mean X = 17.5
Squared deviation from mean Y = 3350
Sum of the product of x and y = 240
Number of observations = 6Marks:2Answer:

Q3
Which symbol do we use to denote Karl Pearson's coefficient of correlation?
Marks:1Answer:
We use small 'r' to denote Karl Pearson's coefficient of correlation.

Q4Marks:3
Answer:
The following are reasons for giving preference to Karl Pearson’s coefficient of correlation over scatter diagram:
 Karl Pearson’s coefficient of correlation measures the precise extent of correlation which is not possible in case of scatter diagram.
 Presence of covariance in the formula makes Karl Pearson’s coefficient of correlation an ideal measure.
 Being a pure number, Karl Pearson’s coefficient of correlation facilitates comparison between series.
 Karl Pearson's measure gives both direction and degree of the relationship between two variables.

Q5
From the following data, compute the coefficient of correlation between X and Y.
X Series: N=7, A.M.=4, ∑x^{2}=28
Y Series: N=7, A.M.=8, ∑y^{2}=76
∑xy=46
Marks:3Answer:
There is a very high positive correlation between the X and Y .