Here is a detailed explanation in paragraph format about Skewness, its meaning, types, measurement methods, and its significance:
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Meaning and Definition of Skewness
Skewness is a statistical measure that describes the asymmetry or distortion of a frequency distribution from a symmetrical bell curve (normal distribution). In a perfectly symmetrical distribution, the mean, median, and mode are all equal. Skewness occurs when one tail of the distribution is longer or fatter than the other. If the distribution is not symmetrical, it is said to be skewed. In technical terms, skewness indicates whether the observations in a dataset are concentrated on one side or spread out on the other.
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Types of Skewness
There are three types of skewness:
1. Positive Skewness (Right-Skewed): In this case, the right tail (higher values) is longer than the left. The mean > median > mode. Most values are concentrated on the left side.
2. Negative Skewness (Left-Skewed): Here, the left tail (lower values) is longer than the right. The mean < median < mode. Most values are concentrated on the right side.
3. Zero Skewness (Symmetrical): The distribution is perfectly symmetrical. The mean = median = mode, indicating no skewness.
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How to Judge Skewness in a Dataset
To determine whether a dataset is skewed:
Compare mean, median, and mode.
Use skewness coefficients or formulas.
Graphical methods like histograms, boxplots, and curves also visually indicate skewness.
A positively skewed distribution has a longer tail on the right, and a negatively skewed distribution has a longer tail on the left.
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Tests or Measures of Skewness
There are two types of measures used to calculate skewness:
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1. Absolute Measures of Skewness
Absolute skewness provides the amount by which a distribution is skewed but not the direction.
Common formulas:
Karl Pearson’s Method:
\text{Skewness} = \text{Mean} - \text{Mode}
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2. Relative Measures of Skewness
Relative measures express skewness as a pure number (unitless), which allows comparison across different datasets.
Important Relative Measures:
Karl Pearson’s Coefficient of Skewness:
\text{Coefficient of Skewness} = \frac{\text{Mean} - \text{Mode}}{\text{Standard Deviation}}
5. Be unaffected by extreme values (in some cases, like Bowley’s method).
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Conclusion
Skewness is an essential concept in descriptive statistics to understand the shape and nature of a distribution. It helps in identifying whether the data is balanced or lopsided, thereby guiding more accurate analysis. Absolute measures show the amount of skewness, while relative measures help in comparing across different datasets. The choice of method depends on data type, size, and whether the mode or median is defined.
