Which of the following is not a measure of dispersion?
C) Arithmetic Mean
D) Standard Deviation
Answer Explanation in Detail
Dispersion plays an very important role for describing the character of variability in data. Only the representative value can be discovered by Average but Dispersion actually finds out how individual value fall apart on an average from the representative value. Some of the major objectives of Dispersion are determining the reliability of central tendency; comparing the consistency of two or more series; determining the cause of variability and controlling it; controlling quality and analyzing the time series.
Measures of Dispersion
Some of the various Measures of Dispersion are as follows:
The difference between Largest and Smallest items in the distribution is called Range. Range is very simple to understand and calculate . The coefficient of Range can be calculated using the formula below:
Coefficient of Range = (L-S) / (L+S)
b) Quartile Deviation or Semi-Inter Quartile Range
Depending upon the lower and upper quartiles , the measure of dispersion is calculated which is called Quartile Deviation. Interquartile Range is the difference between upper and lower quartile. And Half of the Interquartile Range is called Semi- Quartile Range. Quartile Deviation is only the absolute measure of dispersion which indicates that if there is a necessity for comparative study of variability of two distribution then coefficient of quartile deviation is needed.
Quartile Deviation = (Q3-Q2)/2
Coefficient of Quartile Deviation = (Q3-Q1)/(Q3+Q1)
c) Mean Deviation or Average-Deviation
The above discussed two terms (Range and Quartile Deviation) are not considered as better measures of dispersion as all of the items are not included in both cases and they do not show variations of the items from an average that ignores the formation of the distribution. But Mean Deviation shows the variation of items from average.
d) Standard Deviation
Standard Deviation is considered as the best measure of dispersion and is free from the defects of other measures of dispersion.
e) Coefficient of Variation
Coefficient of Standard Deviation is the relative measure of dispersion that is based on the standard deviation. Similarly, 100 times the Coefficient of Standard Deviation is called coefficient of variation which is denoted by CV.
Coefficient of Variation = (Standard Deviation/ Mean) * 100