Numerical Example and Discussions-ECO6416

Numerical Example and Discussions-ECO6416 - Numerical...

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Numerical Example and Discussions A Numerical Example: Given the following, small (n = 4) data set, compute the descriptive statistics: x 1 = 1, x 2 = 2, x 3 = 3, and x 4 = 6. i x i ( x i - ) ( x i - ) 2 ( x i - ) 3 ( x i - ) 4 1 1 -2 4 -8 16 2 2 -1 1 -1 1 3 3 0 0 0 0 4 6 3 9 27 81 Sum 12 0 14 18 98 The mean is 12 / 4 = 3; the variance is s 2 = 14 / 3 = 4.67; the standard deviation is s = (14/3) 0.5 = 2.16; the skewness is 18 / [3 (2.16) 3 ] = 0.5952, and finally, the kurtosis is 98 / [3 (2.16) 4 ] = 1.5. You might like to use Descriptive Statistics to check your hand computation. A Short Discussion on the Descriptive Statistic: Deviations about the mean μ of a distribution is the basis for most of the statistical tests we will learn. Since we are measuring how much a set of scores is dispersed about the mean μ , we are measuring variability . We can calculate the deviations about the mean μ and express it as variance σ 2 or standard deviation σ . It is very important to have a firm grasp of this concept
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Numerical Example and Discussions-ECO6416 - Numerical...

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