Revision

Measures of Dispersion

Outcomes By the end of this lecture, the student will be able to Know definition, uses and types of statistics.

Measures of Dispersion These are methods which used for measuring variability (or homogenicity) of observations.

a) The Range:  It is defined as the highest observation the lowest observation. It is a simple measure, easily and quickly obtained. Sometimes we cannot differentiate between the amount of variation among different groups if they have equal largest and smallest observations.  This results from the fact that this methods neglects all intermediate o

 This results from the fact that this methods neglects all intermediate observations.  e.g. 1 st group: range = 9-1 = 8 2 nd group: range = 9-1 = 8

It is defined as the average of the absolute deviation of each observation from the arithmetic mean N.B. Absolute deviation means difference between two quantities and this difference is given a +ve sign always. It is denoted by Mean absolute Deviation = b) The mean absolute Deviation:

 The range is a good measure of dispersion but it does not have good mathematical properties. Ex : The mean Absolute deviation= 12/5 =

It equals the mean of the squared deviations of observations from their arithmetic mean. S 2 We use (n-1) instead of n as a correction for small values. So, S 2 = c) The variance: (S 2 )

 Mathematically this equation equals to: This formula is better and is easier in computation. It is the on commonly used.

It is defined as the positive Square route or the variance. It should always be defined in the same unit as the original variables. I.For ungrouped data: d) The Standard Deviation: (S)

Ex:

II. Computation of the standard deviation from grouped data: a.Using the long method: Steps  Determine the mid point for each interval.  Find the product for each interval and  the sum of these products.  Find the product for each interval by multiplying  by the corresponding value and then find the sum of these product

 Find the variance S 2 from the formula: Standard Deviation

Ex : Age in years Frequency f j Mid point x j f j x j f j x j Total (Σ)

Assignment TitleStudent Name The Standard Deviation امل محمد احمد احمد اميره اسعد يوسف اميره صلاح مرشدي انجي عبد الموجود

References Biostatistical analysis: Jerrold H. Zar