Page 187 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 2C D
r C (concurrent deviation formula)
D

8.4 Keywords

Bivariate Distribution: When various units under consideration are observed simultaneously,
with regard to two characteristics, we get a Bivariate Distribution
Correlation: When the relationship is of a quantitative nature, the appropriate statistical tool for
discovering and measuring the relationship and expressing it in a brief formula is known as
correlation.
Correlation analysis: Correlation analysis attempts to determine the ‘degree of relationship’
between variables.
Correlation Coefficient: It is a numerical measure of the degree of association between two or
more variables.

Dots of the diagram: Each pair of values (Xi, Yi) is denoted by a point on the graph. The set of
such points (also known as dots of the diagram.
Scatter Diagram: Let the bivariate data be denoted by (Xi, Yi), where i = 1, 2 ...... n. In order to
have some idea about the extent of association between variables X and Y, each pair (Xi, Yi), i =
1, 2......n, is plotted on a graph. The diagram, thus obtained, is called a Scatter Diagram.
Spearman’s Rank Correlation: This is a crude method of computing correlation between two
characteristics. In this method, various items are assigned ranks according to the two characteristics
and a correlation is computed between these ranks.
Univariate Distribution: Distributions relating to a single characteristics are known as univariate
Distribution.

8.5 Review Questions

1. Define correlation between two variables. Distinguish between positive and negative
correlation. Illustrate by using diagrams.
2. Write down an expression for the Karl Pearson’s coefficient of linear correlation. Why is
it termed as the coefficient of linear correlation? Explain.
3. “If two variables are independent the correlation between them is zero, but the converse
is not always true”. Explain the meaning of this statement.
4. Distinguish between the Spearman’s coefficient of rank correlation and Karl Pearson’s
coefficient of correlation. Explain the situations under which Spearman’s coefficient of
rank correlation can assume a maximum and a minimum value. Under what conditions
will Spearman’s formula and Karl Pearson’s formula give equal results?

5. Write short notes on scatter diagram.
6. Compute Karl Pearson’s coefficient of correlation from the following data:
X : 8 11 15 10 12 16
Y : 6 9 11 7 9 12

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