Skewness Definition:
In a symmetrical distribution the class – frequencies decrease to zero symmetrically on either side of a central maximum. This type of distribution is a special case and this form of distribution is comparatively rare. The more common type of distribution of which the symmetrical distribution is a general form is the moderately asymmetrical distribution, also called the skewed distribution. In this type of distribution the class – frequencies decrease with markedly greater rapidity on one side of the maximum than on the other.
The departure of a frequency distribution from symmetry is called its skewness.
Skewness formula:
Several measures have been devised to measure this skewness. Such measures should (a) be pure numbers, so as to be independent of the units in which the variable is measured, and (b) be zero when
the distribution is symmetrical.
Three such measures deserve mention.
In the first place we can define
Skewness = {(Q3 – Me) – (Me – Q1)}/2Q, where Q3 = third quartile, Q1 = first quartile, Me = median and Q = semi inter quartile range. From the formula we clearly see that it is a pure number, because both numerator and denominator have the same dimensions, and it is zero when the distribution is symmetrical. It varies from -1 to +1.
This is a rather rough and ready measure which might, however, be useful if we were using the semi inter quartile range as a measure of dispersion rather than the standard deviation.
The most common measure of skewness is Pearson’s, defined by
Skewness = (Mean – Mode)/standard deviation = (M – Mo)/s
This evidently is a pure number and is zero for a symmetric distribution.
The calculation of this coefficient of skewness is subject to the inconvenience of determining the position of the mode. We may circumvent this difficulty in several ways. For distributions which are obviously not too skew we may use the empirical relation between mean, median and mode.
We then have:
Skewness = 3(Mean – Median)/Standard deviation
Skewness Kurtosis:
Just like how skewness tells us whether a distribution is symmetrical or not, kurtosis skewness tells us whether the hump is flat or not, or in other words, how flat is the hump. That is in comparison with a normal distribution. The higher the kurtosis the steeper is the peak near the mean. And the lower the kurtosis, the flatter is the peak near the mean.
Know more about the online Math help, Math Homework Help. This article gives basic information about Census topic. Next article we will try to cover more statistics help concept and its advantages,problems and many more. Please share your comments.
In a symmetrical distribution the class – frequencies decrease to zero symmetrically on either side of a central maximum. This type of distribution is a special case and this form of distribution is comparatively rare. The more common type of distribution of which the symmetrical distribution is a general form is the moderately asymmetrical distribution, also called the skewed distribution. In this type of distribution the class – frequencies decrease with markedly greater rapidity on one side of the maximum than on the other.
The departure of a frequency distribution from symmetry is called its skewness.
Skewness formula:
Several measures have been devised to measure this skewness. Such measures should (a) be pure numbers, so as to be independent of the units in which the variable is measured, and (b) be zero when
the distribution is symmetrical.
Three such measures deserve mention.
In the first place we can define
Skewness = {(Q3 – Me) – (Me – Q1)}/2Q, where Q3 = third quartile, Q1 = first quartile, Me = median and Q = semi inter quartile range. From the formula we clearly see that it is a pure number, because both numerator and denominator have the same dimensions, and it is zero when the distribution is symmetrical. It varies from -1 to +1.
This is a rather rough and ready measure which might, however, be useful if we were using the semi inter quartile range as a measure of dispersion rather than the standard deviation.
The most common measure of skewness is Pearson’s, defined by
Skewness = (Mean – Mode)/standard deviation = (M – Mo)/s
This evidently is a pure number and is zero for a symmetric distribution.
The calculation of this coefficient of skewness is subject to the inconvenience of determining the position of the mode. We may circumvent this difficulty in several ways. For distributions which are obviously not too skew we may use the empirical relation between mean, median and mode.
We then have:
Skewness = 3(Mean – Median)/Standard deviation
Skewness Kurtosis:
Just like how skewness tells us whether a distribution is symmetrical or not, kurtosis skewness tells us whether the hump is flat or not, or in other words, how flat is the hump. That is in comparison with a normal distribution. The higher the kurtosis the steeper is the peak near the mean. And the lower the kurtosis, the flatter is the peak near the mean.
Know more about the online Math help, Math Homework Help. This article gives basic information about Census topic. Next article we will try to cover more statistics help concept and its advantages,problems and many more. Please share your comments.
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