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
[pic]
[pic]
• Grouped Data
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 :
[pic]
• Ungrouped Data
[pic]
[pic]
• Grouped Data