Coefficient of skewness

[verma.kunal13]

Hello, could someone help me out with my doubt.

On page 21 of CT3, there is coefficient of skewness. In denominator, the variance is calculated by dividing "n" while I think it should be "n-1." Please give me the reason and help me.

thanks.

 

[John Lee]

Hello, could someone help me out with my doubt.

On page 21 of CT3, there is coefficient of skewness. In denominator, the variance is calculated by dividing "n" while I think it should be "n-1." Please give me the reason and help me.

thanks.

All of the sample moments should be divided by n.

It's just that for the sample variance we often (though not always - see Chapter 10) divide by (n-1) to make it an unbiased estimator of σ².

 

[verma.kunal13]

Confusion again

Dear Mr. Lee,

Greetings!

Suppose I have been given data and I have to calculate standard deviation. I will divide it by n-1. In the same question, I have to calculate skewness and coefficient of skewness. Now, should I find out a new SD by dividing it by n rather than n-1. If I use the previously obtained SD, the answers for coefficient of skewness will vary. Kindly help!

Regards,
Kunal Verma

 

[Amit_Bansal]

In such case, you will find out the sample variance by using (n-1) to make it unbiased estimator of the population variance. And while computing skewness & coefficient of skewness, you will use 'n' only.

Remember, Original Second moment is Variance using 'n', but just to make it unbiased estimator [which you'll come to know in details in Ch.10] we use 'n-1'. And Coefficient of skew is defined to be "Third moment divided by Second moment raised to power 3/2" so we just use original definition of variance in Coeff of skew formula.

Moreover we're concerned with +/- sign of coefficient, So n or n-1 doesn't matter much.

 

[Jammy]

Hi,
Could we have further clarity on this topic?

If we're given data (not stated that it's a sample) and have been asked to calculate variance and coefficient of skewness :

1. what will we use for variance (n-1 or n) ?
2. what will we use in the denominator for the coefficient of skewness (n-1 or n) ?

 

[Hemant Rupani]

Hi,
Could we have further clarity on this topic?

If we're given data (not stated that it's a sample) and have been asked to calculate variance and coefficient of skewness :

1. what will we use for variance (n-1 or n) ?
2. what will we use in the denominator for the coefficient of skewness (n-1 or n) ?

1.if you find any clue to the data be exhaustive then divide by n, otherwise n-1 will be good.
2. n.