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Calculate the mean, standard deviation, skewness and the kartosis of the data and comment on it.
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please show steps.
math   Statistics-And-Probability   
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Answer #1

mean = \bar{x}=\frac{\sum_{i}x_{i}}{n} \ \ n=125 \\ so\ \bar{x} = 20.824 \\ sd=s = \sqrt{\frac{\sum (x_{i}-\bar{x})^{2}}{n-1}} = 1.805 \\ skewness = \frac{\sum_{i}(x_{i}-\bar{x})^{3}}{n*\tilde{s}^{3}} \\ \ where \ \tilde{s} = s*\sqrt{(n-1)/n} = 1.7977 \\ so\ skewness = 0.0579 \\ kurtosis = \frac{\sum_{i}(x_{i}-\bar{x})^{4}}{n*\tilde{s}^4} = 2.29 \\

Since kurtosis is not too high, there is expected to be moderately heavy tails, and also skewness is not too high so data will be mostly symmetric.

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