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**CORRELATION**

**Important terms and concepts**

Correlation studies the relationship between tow variables in which change in the value of one variable causes change in the other variable. It is denoted by letter â€˜râ€™.

**Kinds of correlation:-**

1. Positive and Negative correlation.

2. Linear and non â€“ linear correlation.

3. Simple and multiple correlations.

Positive correlation: When both variables move in the same direction. If one increases, other also increases and vice-versa.

**Negative correlation: -** When two variables move in the opposite direction, they are negatively correlated.

**Linear Correlation: - **When two variables change in a constant proportion.

Non- linear correlation: - When two variables do not change in the same proportion.

**Simple correlation â€“** Relationship between two variables are studied.

**Multiple Correction â€“ **Relationship between three or more than three variables are studied.

**Degrees of Correlation:**

1. Perfect Correlation - When values of both variables changes at a constant rate Types â€“ (a) Perfect positive correlation â€“ when values of both variables changes at a constant ratio in the same direction correlation coefficient value (r) is + 1

(b) Perfect negative correlation â€“ When values of both the variables change at a constant ratio in opposite direction. Value of coefficient of correlation is -1

2. Absence of correlation : When there is no relation between the variables r = 0

3. Limited degree correlation : The value of r varies between more than O and less than 1

Types - a) High : r his between Â± 0.7 & 0.999

b) Moderate = r lies between Â± 0.5 and + 0.699

c) Low: r < Â± 0.5

**Different methods of finding correlation**

a) Karl Pearsonâ€™s coefficient method

b) Rank method / Spearmanâ€™s coefficient method

c) Scatter Diagram

(A) Karl Pearsonâ€™s Method

A = assumed mean**Merits of Karl Pearsonâ€™s Method**

1. Helps to find direction of correlation

2. Most widely used method

Demerits of Karl Pearsonâ€™s method

1. Based on large number of assumptions

2. Affected by extreme values

(B) Spearmansâ€™s Rank Correlation Method

Formula

In case of non repeated ranks :-

M = number of items with repeated ranks.

**Merits of Spearmanâ€™s Rank Correlation**

1. Simple and easy to calculate

2. Not affected by extreme values

**Demerits of Spearmanâ€™s Rank Correlation**

1. Not Suitable for grouped data

2. Not based on original values of observations.

(C) Scatter Diagram â€“ Given data are plotted on a graph paper. By looking at the scatter of

points on the graph, degree and direction of two variables can be found.

**Merits of Scatter Diagram**

1. Most simplest method.

2. Not affected by size of extreme values.

**Demerits**

1. Exact degree of correlation cannot be found.

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52 videos|42 docs

### Correlation

- Video | 17:36 min
### Karl Pearson's Coefficient (Part - 2)

- Video | 17:50 min
### NCERT Solutions - Correlation

- Doc | 6 pages
### Scatter Diagram

- Video | 15:37 min

- Karl Pearson's Coefficient (Part - 1)
- Video | 15:10 min
- NCERT Textbook - Correlation
- Doc | 16 pages