absolute and relative measures of dispersion
Absolute Measures of Dispersion
Range: The range of a set of observation is the difference between the
maximum and minimum values.
Quartile Deviation: Quartile deviation is defined as the half of the difference
between the first and third quartiles.
Quartile Deviation: = (Q3 - Q1) / 2.
Mean Deviation: Mean deviation of a set of observations is the arithmetic
mean of the absolute deviations. from mean or any other specified value. Here
we take absolute deviations so that the positive and negative deviations do not
cancel out each other.
Standard Deviation: Standard deviation of a set of observations is the square
root of the arithmetic mean of squares of deviations from arithmetic mean.
Standard deviation is generally denoted by σ and is always is a non negative
number. The square of standard deviation (S.D.) is called variance of a
variable. S.D. and variance of a variable, say x, is denoted by σx and Var(x) or
σ2 respectively.
For ungrouped frequency distribution, the S.D. is given by the following
formula:
properties of S.D. make it superior to other measures of
dispersion.
it is based on all observations. If the value of one observation
changes, the S.D. changes but range and quartile deviation may remain
unaffected due to such a change.
it is least affected by the sampling
fluctuation.
it is easy to be treated algebraically.
given the
S.D. of two different groups S.D. along with the number of observations in
each group and their mean ( arithmetic mean) , the variance for the composite
group can be easily calculated using the following formula:
Relative Measures of Dispersion: These measures are free of unit of
measurement.
Coefficient of Variation = S.D./ Mean × 100
Coefficient of Quartile Deviation = Quartile Deviation / Median × 100
Coefficient of Mean Deviation = Mean Deviation / Mean or Median × 100
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Range: The range of a set of observation is the difference between the
maximum and minimum values.
Quartile Deviation: Quartile deviation is defined as the half of the difference
between the first and third quartiles.
Quartile Deviation: = (Q3 - Q1) / 2.
Mean Deviation: Mean deviation of a set of observations is the arithmetic
mean of the absolute deviations. from mean or any other specified value. Here
we take absolute deviations so that the positive and negative deviations do not
cancel out each other.
Standard Deviation: Standard deviation of a set of observations is the square
root of the arithmetic mean of squares of deviations from arithmetic mean.
Standard deviation is generally denoted by σ and is always is a non negative
number. The square of standard deviation (S.D.) is called variance of a
variable. S.D. and variance of a variable, say x, is denoted by σx and Var(x) or
σ2 respectively.
For ungrouped frequency distribution, the S.D. is given by the following
formula:
dispersion.
it is based on all observations. If the value of one observation
changes, the S.D. changes but range and quartile deviation may remain
unaffected due to such a change.
it is least affected by the sampling
fluctuation.
it is easy to be treated algebraically.
given the
S.D. of two different groups S.D. along with the number of observations in
each group and their mean ( arithmetic mean) , the variance for the composite
group can be easily calculated using the following formula:
Relative Measures of Dispersion: These measures are free of unit of
measurement.
Coefficient of Variation = S.D./ Mean × 100
Coefficient of Quartile Deviation = Quartile Deviation / Median × 100
Coefficient of Mean Deviation = Mean Deviation / Mean or Median × 100
thank you for visiting idea tutors. you can ask your questions in the comment box. if you want to request any study material regarding these topics you can contact us via form or put the topic inthe comment box
really helpful post thank you
ReplyDeleteNice information plz add more statistics topics and videos if possible
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