What is Quartile Deviation (QD) and Standard Deviation (SD)?

Quartile Deviation.

The quartile deviation is a slightly better measure of absolute dispersion than the range. The quartile deviation is half the difference between the upper and lower quartiles in a distribution.

It is a measure of the spread through the middle half of a distribution. It is also known as inter-quartile range. But it ignores the observation on the tails. It can be useful because it is not influenced by extremely high or extremely low scores.

Quartile Deviation is an ordinal statistic and is most often used in conjunction with the median. Quartile deviation is denoted as Q.

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Merits and limitations Quartile Deviation:

ft is a simple measure of dispersion. QD is most relevant to find out the dispersion of the distribution when the measure of central tendency is taken as median. QD is more useful than range because QD speaks about the 50% of the scores of a distribution, while range speaks about the highest and lowest scores.

It provides reliable results since it uses middle 50% of scores. In case of open-end distribution QD is more reliable as compared to other measures of dispersion. QD should not be used in further mathematical computations. It is also not useful to study in each and every statistical situation.

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Standard Deviation:

It is a measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance the mean of the squared deviations of the individual observations from the mean. The standard deviation of the sample and population is denoted by s and s, respectively

Merits of Standard Deviation:

Standard deviation is least affected by fluctuation of sampling. It is calculated on the basis of all observations. It is amenable to further mathematical computations.