Measures of Variability Range Standard Deviation Variance

Standard Deviation Standard Deviation: A measure of the spread of the scores around the mean. Average distance from the mean. Example: Can you calculate the average distance of each score from the mean? (X=4) 7, 6, 3, 3, 1 (distance from the mean: 3,2,-1,-1,-3) 3, 4, 4, 5, 4, (distance from the mean: -1,0,0,1,0)

Formula for Standard Deviation s =  (X i -X) 2 n-1 Standard deviation of the sample Sigma: sum of what follows Each individual score Mean of all the scores Sample size

Why n-1? s (lower case sigma) is an estimate of the population standard deviation (  :sigma). In order to calculate an unbiased estimate of the population standard deviation, subtract one from the denominator. Sample standard deviation tends to be an underestimation of the population standard deviation.

Variance Variance: Standard deviation squared. S =  (X-X) 2 n-1 Not likely to see the variance mentioned by itself in a report. Difficult to interpret. But it is important since it is used in many statistical formulas and techniques.

X ( x-x) ( x-x) ∑

SD concept in Finance Standard deviation is a standard measure of investment risk. It is a historical statistic measuring volatility and the dispersion of a set of data from the mean. Standard deviation is a measure of the volatility, or how far away from the mean the outcomes will be. A small-cap stock will typically have a high standard deviation compared to a stable blue chip dividend stock. The small-cap stock may have a higher expected rate of return but that is to compensate the owner for a greater amount of risk.

There are two routes for a worker to reach his office. Both the routes involve hold ups due to traffic lights. He records the time it takes over a series of six journeys for each route. The results are shown in the table. Route Route Using your answers to Route 1 and Route 2 suggest which route you would recommend. State your reason clearly.

Grouped Data X f fx (X-X ) (X-X) 2 f(X-X) 2

Coefficient of Variation The SD is an absolute measure of dispersion that expresses variation in the same unit as the original data. The SD cannot be sole basis for comparing two distributions. If we have SD of 10 and mean of 5 the value is twice as large as mean itself. But if we have SD of 10 and mean of 5000 the variation relative to mean is insignificant. The CV is relative measure of dispersion. IT relates SD and mean by expressing SD as percentage of mean. The unit of measurement is percentage.

CV (P)=(SD/µ)*100 Technician A completes on an average 40 analysis with a SD of 5. Technician B completes on an average 160 analysis with a SD of 15.