GATE (Graduate Aptitude Test in Engineering) Psychology Research Methods and Statistics-Statistics in Psychology Study Material (Page 4 of 9)

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# Measures of Variation or Dispersion: Range and Mean Deviation

Dispersion measures the extent to which scores differ from one another and from mean of the distribution. It provides a measure of variability. Range, variance, and standard deviation are considered as major measures of variation.

When all observation sets are equal, dispersion is zero. In case of higher discrepancy, dispersion is more. Measures of dispersion numerically depict extent of variability of individual observations. For probability distributions, dispersion measures the spread.

## Range

Spread of scores in a distribution is known as range. Subtraction…

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# Measures of Variation or Dispersion: Variance and Standard Deviation

## Variance

Measure of variation around mean calculated as squared deviation scores about mean of a distribution is known as variance. That is, . Since we know that frequency of unique deviation scores, this is same as and simplified to .

## Standard Deviation

Standard deviation was given by Karl Pearson in 1823. It is useful and widely used measure of absolute dispersion. The square root of the variance is known as Standard Deviation (s) . That is, .

Deviation Score (d)
| d^{2} × Frequency |

10 - 5.6 = 4.4 | 19.36 × 1 = 19.36 |

9 - 5.6 = 3.4 | 11.56 × 3 = 34.68 |

8 - 5.6 = 2.4 | 5.76 × 3 = 23.04 |

7 - 5.4 = 1.4 | 1.96 × 5 = 9.80 |

6 - 5.4 = 0.4 | 0.16 × 8 = 1.28 |

5 - 5.6 =-0.6 | 0.36 × 7 = 2.52 |

4 - 5.6 =-1.6 | 2.56 × 5 = 12.80 |

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