Shape Characteristics:
1. Skewness
2. Kurtosis
Skewness:
Skewness is a statistical measure that assesses the asymmetry of a probability distribution. It
quantifies the extent to which the data is skewed or shifted to one side.
Positive skewness indicates a longer tail on the right side of the distribution, while negative
skewness indicates a longer tail on the left side. Skewness helps in understanding the shape and
outliers in a dataset.
In statistics, skewness is a degree of asymmetry observed in a probability distribution that
deviates from the symmetrical normal distribution (bell curve) in a given set of data.
Types of Skewness
Symmetric:
When data is symmetrically distributed, the left-hand side, and right-hand side, contain the same
number of observations. (If the dataset has 90 values, then the left-hand side has 45 observations,
and the right-hand side has 45 observations.).
Positive Skewed or Right-Skewed (Positive Skewness)
In statistics, a positively skewed or right-skewed distribution has a long right tail. It is a sort of
distribution where the measures are dispersing, unlike symmetrically distributed data where all
measures of the central tendency (mean, median, and mode) equal each other. This makes
Positively Skewed Distribution a type of distribution where the mean, median, and mode of the
distribution are positive rather than negative or zero.
Negative Skewed or Left-Skewed (Negative Skewness)
A negatively skewed or left-skewed distribution has a long left tail; it is the complete opposite of
a positively skewed distribution. In statistics, negatively skewed distribution refers to the
distribution model where more values are plots on the right side of the graph, and the tail of the
distribution is spreading on the left side.
In negatively skewed, the mean of the data is less than the median (a large number of data-pushed
on the left-hand side). Negatively Skewed Distribution is a type of distribution where the mean,
median, and mode of the distribution are negative rather than positive or zero.
Calculation of symmetricity:
If Rule of thumb: The skewness is between -0.5 & 0.5, the data are nearly symmetrical.
If the skewness is between -1 & -0.5 (negative skewed) or
between 0.5 & 1(positive skewed), the data are slightly skewed.
If the skewness is lower than -1 (negative skewed) or greater than 1 (positive skewed), the data are
extremely skewed.
Box plot:
Determine skewness from Box plot:
Determine skewness from Steam-and-leaf plot:
Kurtosis:
kurtosis is a measure of the tailedness of a distribution. Tailedness is how often outliers occur.
• Distributions with medium kurtosis (medium tails) are mesokurtic.
• Distributions with low kurtosis (thin tails) are platykurtic.
• Distributions with high kurtosis (fat tails) are leptokurtic.
