Measures of dispersion
•Mean absolute deviation
•Co-efficient of variation
Difference between highest & lowest scores of distribution.
• E.g. 3,5,7,9,12. Range = 12-3=9.
• Easy to compute and understand.
• Quick impression of dispersion.
• Useful for SD.
• It is sensitive to extreme value
• It dose not give you any information about the pattern of
• It is based on two variable.
Mean absolute deviation (MD)
• MD=∑│ │/n
• ∑│ │ │= absolute deviation of each score from
the mean ignoring plus or minus sign.
• n= Total number of scores.
• Calculate the difference between each item &
the mean. (X - ).
• Sum up the values of the difference ignoring
plus and minus sign.
• MD= 12/5 = 2.4
• Evaluation –
• It represents the overall dispersion.
• MD value is not amenable to mathematical
• Hence MD is not useful for advance statistical
• These measures are based on the square
deviation of all values from the mean.
• It eliminates the drawback of MD
• The variance is the means of the squared
deviations from the mean of distribution.
• Mean Variance SD CV
• MD= σ 2 = σ = CV
• σ 2 or S2 = ∑ 2 / n
• σ 2 or S2 = ∑ 2 / n
• It express the average dispersion not in the
original units of measurements but in squared
• The problem is solved by taking the square root
of variance .
• This transform into SD
• It is the square root of the means of the
squared deviation from the mean of
• It express dispersion in the original scores.
• It is originally denoted by σ, the Greek letter
Sigma or S .
• SD is more stable from sample to sample.
• It is possible to obtain SD for two or more
• It is more useful in more advanced analysis i.e.
to calculate co -efficient of variation.
Co-efficient of Variation
• SD can’t be compared in absolute magnitudes
when the distribution compared have different
• E.g. mean of 7 than to mean of 75, it would
convey different meaning.
• Therefore the degree of variability must be
calculated in relation to the mean of the
• This is measured by coefficient of variation.
• CV indicates the relative variation.
• Democratic participation in four co-operatives
• There are no significant differences among the SD in
the four cooperatives.
• However there are substantial differences between
the means of indicating the varying degrees of
democratic participation in each co operative.
Co operative A-160 B-150 C-190 D-170
Mean 4.7 5.4 2.9 5.6
SD 2.7 2.9 2.8 2.7
CV 57 % 54 % 95.5 % 48 %
• When the value of coefficient of variation is
higher, it means that the data has high variability
and less stability. When the value of coefficient of
variation is lower, it means the data has less
variability and high stability.
• CV shows that the relative deviation from the
mean is higher in ‘c’ than in other co operatives,
reflecting the given lower degree of Homogeneity
in democratic participation i.e. higher degree of
variability in democratic participation it.
• The lower the value of the coefficient of
variation, the more precise the estimate.
• The advantage of the CV is that it is unit less.