Question

explain the term measure of dispersion and state briefly two advantages and two disadvantages of using each of the following measures range, mean deviation and standard deviation

Answer 1

Here I will define measure of dispersion in two definitions.

Measure of dispersion: a) The measure s which express the spread of observations in terms of distance between the values of selected observations. These are also termed as distance measure. For example range.

b) The measures which express the spread of observations in terms of the deviations of observations  from some central value. For example Mean deviation and standard deviation.

RANGE : ADVANTAGE 1) SIMPLE MEASURE OF DISPERSION

2) EASY TO CALCULATE AND UNDERSTAND.

DISADVANTAGE: 1) Since it is based on extreme observations which are subjects to chance fluctuations.

2) Not reliable measure of dispersion. We cannot rely on it.

MEAN DEVIATION: ADVANTAGE: IT IS BASED ON ALL THE OBSERVATIONS IT IS THEREFORE BETTER THAN RANGE.

DISADVANTAGE: It ignores the sign of the deviation , creates artificiality and therefore useless for further mathematical treatment.

3) STANDARD DEVIATION

ADVANTAGE:1) BASED ON ALL THE OBSERVATIONS

2) AFFECTED VERY LITTLE BY FLUCTUATIONS OF SAMPLING.

3) STEP OF SQUARING OVERCOMES THE DRAWBACK OF IGNORING THE SIGN IN MEAN DEVIATION.

DISADVANTAGE: 1) STANDARD DEVIATION GIVES GREATER WEIGHT TO EXTREME VALUES.