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Author | Topic: Kurtosis Calc Question |
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bobert@2013-05-16 10:14:35 |
Hi, I am doing some brush up work on sd, var, skew, and kurtosis while using Excel07 as a check to myself. I was alright up until Kurtosis. My answer is a bit off from the Excel calculated value. My data consists of 16 values, eight 1's and eight 2's. I wanted it to be normally distributed, and it is also a sample. Up to now I have gotten: Avg = 1.5 MAD = .5 SD = .5164 Var = .2667 Skew = 0 Rounding is done to the .0001 The formula I am using for Kurtosis is: ((1/n) * Sum(Xi-Avg(X))^4 / s^4) - 3 The pieces then come out to be: 1/n = 1/16 = .0625 Sum(Xi-Avg(X))^4 = 1 Note: This has to be correct up to this point because being as the values were only 1 and 2, the X-Avg(X) has to be -.5 and .5 respectively which to the 4th will be the same at .0625 as well or 1/16th. This I all understand. No real difference than with anything else. s^4 = .5164^4 = .0711 Mush that all together and you have: (.0625*(1/.0711))-3 I am doing this step by step to see if anyone can pinpoint where I go wrong. The above = .8789-3 = -2.1211 Excel calculates it to: -2.3077 My first concern is the obvious discrepancy between the two answers, which even if I calculate it using cell results so not to lost on the decimals, I still get -2.12109375 which is about -2.1211. My second concern is that since there is an equal amount of 1's and 2's, shouldn't it be mesokurtic, and have 0 excess kurtosis? I am lost on this. Any help is really appreciated. Thanks. -Bob |