Calculating Skewness and Kurtosis
Skewness is when a distribution is asymmetrical or lacks symmetry. The skewed portion is the long, thin part of the curve. Many researchers use skewed distribution to mean that the data are sparse at one of the distribution and piled up on the other end. An example is like the grades on a particular test that a teacher gives. The grade distribution is skewed, meaning that few students scored at one end of the grading scale, and many students scored at the other end. Like the relationship of A’s to C’s and B’s. It is more probable that you would have more C’s and B’s compared to A’s. So the tail of the skewed graph would be more of a bell towards the B’s and C’s. And the tapered off end would be the portion of the class that had gotten an A.The concept of skewness helps us to understand the relationship of the mean, median, and the mode. Now when graphing the skewness the mode is considered the high point or the apex. The mean tends to be located toward the tail of the distribution . . .
The largest value in the distribution In conclusion the last point I would like to make: the skewness and kurtosis in statistics, like all the descriptive statistics, are designed to help us think about the distributions of scores that our tests create. Unfortunately, I can give you no hard-and-fast rules about these or any other descriptive statistics because interpreting them depends heavily on the type and purpose of the test being analyzed. Distributions with thinner than normal tails are "platykurtic". Distributions with normal tails are "mesokurtic. A distribution may have no skew - that is, may be symmetrical - yet still not be normal. This is a diagram that utilizes the upper and lower quartiles along with the mean and the two most extreme values to depict a distribution graphically. Then divide the total by the standard deviation. Nonetheless, I have tried to provide some basic guidelines here that I hope will serve you well in interpreting the skewness and kurtosis statistics when you encounter them in analyzing any data. From the lower and upper quartiles, lines referred to as whiskers are extended out from the box toward the outermost data values. Now the coefficient of skewness measures the degree of skewness that exists in a distribution of numbers. If negative then it is negatively skewed.
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