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Analysis of Frequency Distributions - Comparison of Two Frequency Distributions with Same Mean

notes

Let `bar x_1 `and `σ_1` be the mean and standard deviation of the first distribution, and bar `x_2` and `σ_2` be the mean and standard deviation of the second distribution. 
Then C.V (1st distribution) = `σ_1/bar x_1 xx 100`
and  C.V (2nd distribution)  = `σ_2/bar x_2 xx 100`
Given bar `x_1 = bar x_2 =  bar x `  (say)

Therefore C.V (1st distribution) = `σ_1/bar x xx 100`   ...(1)
and  C.V (2nd distribution)  = `σ_2/bar x  xx 100`          ...(2)
It is clear from (1) and (2) that the two C.Vs. can be compared on the basis of values of `σ_1` and  `σ_2` only.
Thus, we say that for two series with equal means, the series with greater standard deviation (or variance) is called more variable or dispersed than the other. Also, the series with lesser value of standard deviation (or variance) is said to be more consistent than the other. 

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