Measures of Dispersion

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MEASURES OF DISPERSION

I. Meaning and Types of Measures of Dispersion

Measures of Dispersion ( Variation or Spread )
- is a measure used to describe the variation of a set of data

|Measure of Dispersion |Symbol for | | |Parameter |Sample | |A. ABSOLUTE DISPERSION | | | |Range |R |R | |Average Deviation |A.D. |A.D. | |Variance |δ2 |s2 | |Standard Deviation |Δ |s | |Others | | | |B. RELATIVE DISPERSION | | | |Coefficient of Variation |C.V. |c.v. | |Standard Score | | |

II. ABSOLUTE DISPERSION

A. RANGE
Meaning: Range is the difference between the highest and lowest values of the set of data.

Formula for Range :

• Ungrouped Data
R = highest observation minus lowest observation
R = H.V. – L.V.
• Grouped Data
R = highest ucl – lowest lcl

B. VARIANCE and STANDARD DEVIATION

Meaning:Variance is the mean of the squared deviation from the mean.

Standard Deviation is the positive square root of variance.

Formula for Variance and Standard deviation :

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• Ungrouped Data

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• Grouped Data

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Example of computation for ungrouped data

Given: Weights of randomly selected students in pounds:
180, 140, 85, 135, 140, 90, 115, 120, 145, 135, 160, 99, 127

a) Computation of Range

R = H.V. – L.V. = 180 – 85
R = 95 pounds

Interpretation: The gap between the heaviest and lightest weights of students is 95 pounds.

b) Computation of Variance and standard deviation

|Xi |[pic] | |Xi2 |[pic] | | |[pic] | |180 |[pic] | |32400 |[pic] | | | | |140 |[pic] | |19600 |[pic] | | |Note: final answers are expressed to 2 decimal | |85 |places. | |7225 | | | | | |135 | | |18225 |...
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