Question

If efx = 200, efx² = 3280 and ef= 20 find the standard deviation and its coefficient

Answer 1

The standard deviation is 111.64 and its coefficient is 2.791%.

Step-by-step explanation:

a) To find the standard deviation, we can use the formula: Standard Deviation = sqrt(Var) where Var is the variance.

The formula for variance is: Var = (Sum of (x - mean)^2) / n

First, let's calculate the mean:

mean = e*f = 200 * 20

= 4000.

Next, let's calculate the variance:

Var = [(200^2 * 20) + (3280 - 4000)^2] / (20 + 1)

= 262160 / 21

= 12484.762.

Finally, the standard deviation is:

Standard Deviation = sqrt(12484.762)

= 111.64.

b) To calculate the coefficient of standard deviation, we can use the formula:

Coefficient of Standard Deviation = (Standard Deviation / Mean) * 100.

Plug in the values:

Coefficient of Standard Deviation

= (111.64 / 4000) * 100

= 2.791%.