Definition of Standard Deviation

Question

Hi,

I've seen in this forum many times in which de standard deviation is defined as:

SD= sqrt{ /n} with xm being the mean, and n the number of elemets of the set.

However, from a strict point of view, the correct definition is that but with the denominator being n-1, which is called "the Bessel's correction", and has statistical reasons.

I wonder which definition does GMAT tests?

Thanks.

Bunuel · Answer

math-standard-deviation-87905.html

noboru · Answer

Thanks.

I had already checked that post, and I was asking it just in case...

philiptraum · Answer

The correct formula depends on whether or not you are taking the standard deviation of a population or a sample. If it's a population you divide by N, the total population. If it's a sample you divide by n-1, the size of the sample minus 1.

I have no idea which one the GMAT tests but both are correct.

I have no idea which one the GMAT tests but both are correct.

Bunuel · Answer

You certainly don't need to know the difference between sample standard deviation and population standard deviation formulas (the one tested on the GMAT, with N in denominator). Also note that the GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Check this: math-standard-deviation-87905.html

philiptraum · Answer

Ahh thank you bunuel :-)

Posted from my mobile device

AdamKnewton · Answer

Just to echo what Bunnel said: Neither formula is actually used on the GMAT, because you will never be asked to calculate the Standard Deviation of a set. The best definition of SD that you should have going into the test is: "How widespread a given set is." Thus, (2, 4, 6, 8, 10) has a larger standard deviation than (11, 12, 13, 14, 15) because it is more spread-out.

mrbrad · Answer

For reference -- if you ever need to calculate the standard deviation without having all of the data points in a set, you can compute s.d. by first converting back to variance and calculating the weighted summation with the new dataset.

Given the a population with known (1) mean  u_o_l_d ], (2) standard deviation  sd_o_l_d ], and (3) number of samples  n ], when adding a new sample ( x ) into the dataset, the new standard deviation  sd_n_e_w ] may be calculated as follows: 
 sd_n_e_w = \sqrt{\frac{n-1}{n}*(sd_o_l_d)^2 + \frac{1}{n+1}*(u_o_l_d - x)^2}

Of course, the new mean is the simple calculation:
 u_n_e_w = \frac{u_o_l_d*n + x}{n+1}

I know it's not so useful for the GMAT; thought I'd share it either way.

Definition of Standard Deviation

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