**Overview**

Basically correlation is the measurement of the strength of a linear relationship between two variables.

In other words, we define it as- if the change in one variable affects a change in other variable, then there will be a corr. between two variables

Example

1. A person’s income and expenditures.

2. As the temperature goes up, the demand of ice cream also go up.

**Classification**–

**Positive correlation-** When both variables move in the same direction, or if the increase in one variable results in a corresponding increase in the other. this is the condition of positive corr.

**Negative correlation**:

When one variable increases and other decreases or vise-versa.

**No correlation**:

When two variables are independent and do not affect each other then there will be no corr. between the two and this ia the condition of no-correlation.

**Note- (Perfect correlation)**– When a variable changes constantly with the other variable, then there will be perfect corr.

**Scatter plots or dot diagrams**

Scatter or dot diagram is used to check the corr. between the two variables.

It is the simplest method to represent a bivariate data.

When the dots in diagram are very close to each other, then we can say that there is a fairly good corr.

If the dots are scattered then we get a poor corr.

**Karl Pearson’s method** for correlation

We also call Karl Person’s coefficient of corr. as product moment correlation coefficient.

It is denoted by ‘r’, and defined as-

Here and are the standard deviations of these series.

Alternate formula-

Note-

1. The value of ‘r’ lies between -1 and +1.

2. ‘r’ is independent of change of origin and scale.

3. If the two variables are independent then the value of r will be zero.

Value of correlation coefficient (r) | Type of correlation |

+1 | Perfect positive corr. |

-1 | Perfect negative corr. |

0.25 | Weak positive corr. |

0.75 | Strong positive corr. |

-0.25 | Weak negative corr. |

-0.75 | Strong negative corr. |

0 | No corr. |

## Solved exampled of correlation coefficient

**Example: The data given below is about the marks obtained by a student and hours she studied.**

**Find the corr. coefficient between hours and marks obtained. **

Hours | 1 | 3 | 5 | 7 | 8 | 10 |

marks | 8 | 12 | 15 | 17 | 18 | 20 |

Solution:

Let hours = x and marks = y

Karl Person’s formula is given by-

The correlation coefficient between hours and marks obtained is- 0.98

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