Measures of Dispersion


In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are:
• Standard Deviation
• Variance
• Inter-Quartile Range

Which of the two shooters has high dispersion? Why?

Why Deviation measure is required?

Standard Deviation & Variance
Standard Deviation• is a measure used to quantify the amount of variation or dispersion of a set of data values • Often represented as SD, Greek letter σ (sigma) or the Latin letter s

Variance & Coefficient of Variation

Variance• is Square of Standard Deviation often represented as:

Coefficient of Variation (CV)• is a measure of relative variability
It is measured as the ratio of the• standard deviation to the mean
Useful for comparison of variability between two variables or two test
Can be used for comparison only for ratio• -scale variables

Range & Inter-Quartile Range

Range = Largest Value – Smallest Value

• Interquartile range (IQR), also called the midspread or middle 50%
• A measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles
• IQR = Q3 − Q1

CoV example

Suppose you have option to invest in Stock A or Stock B. The stocks • have different expected returns and standard deviations. The expected return of Stock A is 15% and Stock B is 10%. Standard Deviation of the returns of these stocks is 10% and 5% respectively.

Which is better investment?

Stock B would be better investment as its • CoV (5% / 10% = 0.5) is less than the CoV of Stock A (10% / 15% = 0.67)