Question

The first two raw moments of a frequency distribution are 1 and 10 respectively. Find the variance of the distribution.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The variance is 10.

Given

1. First raw moment of the frequency distribution= 1
2. Second raw moment of the frequency distribution. = 10

To Find

The variance of the frequency distribution.

Solution

"The raw moment of any frequency distribution is the moment of any function taken about the mean of the function"

First raw moment (μ₁) = μ₁' = 1                            

Second Raw moment(μ₂) =  μ₂' - (μ₁')² = 10      

Here,

μ₁ and μ₂ are the first and second raw moments

while μ₁' and μ₂' are the first and second central moments respectively

Now for any frequency distribution,

Variance = μ₂' - (μ₁')²,

i.e the second raw moment.

Hence, Variance is 10

Therefore, the variance is 10.

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