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The standard deviation (sigma) of variat...

The standard deviation `(sigma)` of variate x is the square root of the A.M. of the squares of all deviations of x from the A.M. observations.
If `x_i//f_i`, i=1,2,… n is a frequency distribution then `sigma=sqrt(1/N Sigma_(i=1)^(n) f_i(x_i-barx)^2), N=Sigma_(i=1)^(n) f_i` and variance is the square of standard deviation. Coefficient of dispersion is `sigma/x` and coefficient of variation is `sigma/x xx 100`
The standard deviation for the set of numbers 1,4,5,7,8 is 2.45 then coefficient of dispersion is

A

4.9

B

2.04

C

0.49

D

2.45

Text Solution

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The correct Answer is:
To solve the problem step by step, we will find the coefficient of dispersion using the given standard deviation and the mean of the data set. ### Step 1: Calculate the Mean (x̄) The mean (x̄) is calculated by summing all the values in the data set and dividing by the number of values. Given data set: 1, 4, 5, 7, 8 \[ \text{Mean} (x̄) = \frac{1 + 4 + 5 + 7 + 8}{5} = \frac{25}{5} = 5 \] ### Step 2: Use the Standard Deviation (σ) We are given that the standard deviation (σ) is 2.45. ### Step 3: Calculate the Coefficient of Dispersion The coefficient of dispersion is calculated using the formula: \[ \text{Coefficient of Dispersion} = \frac{\sigma}{x̄} \] Substituting the values we have: \[ \text{Coefficient of Dispersion} = \frac{2.45}{5} \] ### Step 4: Perform the Division Now we perform the division: \[ \text{Coefficient of Dispersion} = 0.49 \] ### Conclusion Thus, the coefficient of dispersion is 0.49. ---
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