Range, Quartile Deviation, Mean Deviation & Standard Deviation

1. Range:

Difference between Smallest & Largest value,

R = L-S

Higher Vaqlue of Range implies Higher Dispersion & Vice-versa.

2. Quartile Deviation:

i. The quartile deviation is a slightly better measure of absolute dispersion than the range, but it ignores the observations on the tails.

ii. If we take difference samples from a population and calculate their quartile deviations, their values are quite likely to be sufficiently different.

Quartile Deviation= (Third Quartile-First Quartile)=Q3-Q1/2

3. Mean & Standard Deviation:

i. Two measures which are based on deviation of values from average is called mean deviation.

ii. Since Average is central Value .Some Deviations are +ve & Some are -ve.

iii. If these are added sum will not reveal anything.

iv. In fact Sum of deviations from arithmetic mean is always Zero, mean deviation tries to overcome this problem by ignoring the signs of deviation.

v. It Considers all deviation positive:

Mean Deviation = Modulus (Observation-Arithmetice Mean)/No of Observations