# NCERT Class 12 Practical Geography Chapter 2 Data Processing YouTube Lecture Handouts Part 4

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## Standard Deviation of Grouped Data Long & Short Method Quick Trick Method

### Standard Deviation (Grouped Data)

Class | Mid-point | Unit
| ||

0 - 10 | 2 | |||

10 - 20 | 4 | |||

20 - 30 | 3 | |||

30 - 40 | 1 | |||

40 - 50 | 5 |

### Standard Deviation (Grouped Data)

Class | Mid-point | Units
| |||

0 - 10 | 2 | ||||

10 - 20 | 4 | ||||

20 - 30 | 3 | ||||

30 - 40 | 1 | ||||

40 - 50 | 5 |

### Finding Mean First

Class | Mid-point | Units
| |||

0 - 10 | 2 | ||||

10 - 20 | 4 | ||||

20 - 30 | 3 | ||||

30 - 40 | 1 | ||||

40 - 50 | 5 |

### Standard Deviation (Grouped Data)

Class | Mid-point | Units (f) | ||

0 - 10 | 2 | |||

10 - 20 | 4 | |||

20 - 30 | 3 | |||

30 - 40 | 1 | |||

40 - 50 | 5 |

### Coefficient of Variation

## Correlation

- Knowing the nature of relationship or interdependence between two or more sets of data. It has been found that the correlation serves useful purpose. It is basically a measure of relationship between two or more sets of data. Since, we study the way they vary, we call these events variables. Thus, the term correlation refers to the nature and strength of correspondence or relationship between two variables. The terms nature and strength in the definition refer to the direction and degree of the variables with which they co-vary.
- With the increase in input the output also increases.
- With the increase in the input the output decreases.
- Change in the input does not lead to change in the output.

- For every increase of one unit on the X-axis, there is a corresponding decrease of two units on the Y-axis. It is an example of a negative correlation. It means that the two variables have a tendency to move opposite to each other, i.e.. , if one variable increases, the other decreases and vice versa
- The maximum degree of correspondence or relationship goes upto 1 (one) in mathematical terms. On adding an element of the direction of correlation, it spreads to the maximum extent of – 1 to + 1 through zero. It can never be more than one. The spread can also be translated into linear shape. Correlation of 1 is known as perfect correlation (whether positive and negative) . Between the two points of divergent, perfect correlations lies 0 (zero) correlation, a point of no correlation or absence of any correlation between the variables.
- Larger is the scattering, weaker is the correlation. Smaller is the scattering, stronger is the correlation, and when the plotted points fall on a straight line, the correlation is perfect

### Spearman՚s Rank Correlation

50 | 15 | ||||

40 | 58 | ||||

15 | 26 | ||||

18 | 45 | ||||

20 | 14 |

= rank correlation

= Sum of squares of differences between 2 sets of ranks

N = number of pairs of X-Y

In rho, we obtain a correlation, which makes a good substitute for other types of correlations, when the number of cases is small. It is almost useless when N is large, because by the time all the data are ranked, other type of correlation could have been calculated

✍ Manishika