Variability | Measure of Variability

by Yuvi - August 5, 2023

Measures of Central Tendency are valuable statistical measures but represent only one characteristic of the data i.e. tendency to pile up near the middle of the distribution.

So they are incomplete and fail to reveal the entire story as decision-making requires much more information than this So further statistical analysis is necessary which is in the form of measures of variability which show the extent to which the scores of scattered or spread from the measures of central tendency.

Variability

A measure of Variability is an indicator showing the extent to which the scores tend to scatter or spread about the centre of the distribution i.e. about a measure of Central Tendency. Also called measures of Second Order.

The measures of Variability are

The Range.
The Quartile Deviation.
The Mean/Average Deviation.
The Standard Deviation.

Standard Deviation is the most reliable index of Variability because

Other deviations disregard the signs of values and treat all deviations as positive whereas Standard Deviation squares the values.
Moreover the squared deviations taken for computing SD are taken from the Mean which in itself is an accurate and reliable measure of central tendency.

Range

Meaning – It is the difference between the highest score and the lowest score in the distribution.

Eg. Grp = 40, 42, 50, 56, 70, 86, 90.

Range = 90 – 40 = 50.

Characteristics

It is the most simple and crude measure of variability.
It gives only an approximate or rough indication of variability because it is possible that 2 distributions may have the same range and yet have different variabilities.

Eg. Grp A – 10, 20, 30, 40, 50, 60, 70, 80, 90.

Grp B – 10, 50, 55, 75, 76, 79, 81, 83, 90.

It takes into account only 2 extreme scores so any change in these two will cause a fluctuation. Thus it is a highly unreliable measure.
Cannot be used for grouped data as individual items lose their identity.