The measure of the distance of the data shows how far the data is spread from the average. The measure of the space of the data also shows the diversity of observations indicated by the deviation.
There are several measures to determine data distribution, such as range, quartile deviation, mean deviation, and standard deviation. Measures of central tendency (mean, median, mode) represent frequency distribution values.
Still, these measures do not provide a complete picture of how the observed data are spread over the central value. A measure of central tendency alone is not enough to describe the frequency distribution.
In addition, we must have a measure of the distribution of observational data. An example of data distribution can be detected through data deviations such as skewness and kurtosis.
Intro to Normal Distribution
A normal distribution, also known as the Gaussian distribution or bell curve, is a type of continuous probability distribution that describes the distribution of data points around a central mean value.
It is characterized by a symmetric shape, with the majority of data points clustering around the mean, and the number of data points decreasing as you move further away from the mean.
In a normal distribution, the probability of a random variable that can take on any value is defined by a continuous curve.
The curve is bell-shaped, with the peak at the mean, and the data is symmetrically distributed on either side of it. The mean, median, and mode are equal to each other or lie close to each other.
Examples of normal distributions can be found in various fields, such as biology, finance, and engineering. Some examples include blood pressure of people, IQ scores, and salaries.
These types of data often follow a normal distribution, with most values clustering around the mean and fewer values deviating from it.
Skewness and Kurtosis Measurement
Skewness and Kurtosis are statistical measures that describe the shape of a probability distribution. Skewness measures the degree of asymmetry of a distribution, indicating the direction and extent to which a distribution deviates from symmetry.
On the other hand, Kurtosis is a measure of peakedness of a distribution, indicating how much of the data is concentrated in the tails of the distribution.
It compares the shape of a distribution to that of a normal distribution, which is a commonly used reference distribution. A higher kurtosis indicates more data in the tails, while a lower kurtosis indicates less data in the tails.
Understanding these measures can help in understanding the characteristics of a data set, and how it deviates from a normal distribution.
What is Skewness
Skewness is a measure of asymmetry in the distribution of da, especially in the distribution of values. The skewness sign is represented by a positive, negative, or even zero value.
Skewness with a positive value means that the tail of the distribution is to the right of the highest value. This means most of the distribution is at a low discount.
Negative skewness means that the bottom of the distribution is on the left, indicating that most of the values are on the right side of the curve.
While skewness is zero, the values are distributed symmetrically, with the distance between the right and left tails of the distribution being the same.
Skewness is also interpreted as an allusion to the tendency of the distribution, which determines the symmetry of the mean or average.
The curve is extended to the left or right in a skewed distribution. So, when the plot is more developed to the right side, it shows a positive slope, where mode < median < mean.
On the other hand, when the property is stretched more towards the left direction, it is called negative skewness and mean < median < mode.
Skewness Criteria
Criteria for knowing the distribution model of the slope coefficient:
- If the slope coefficient is <zero, then the shape of the distribution is negative (the left tail is longer).
- If the slope coefficient = zero, then the shape of the distribution is symmetric.
- If the slope coefficient > zero, then the shape of the distribution is positive (the right tail is longer).
For example, the skewness value of the system security variable shows average data when these values are in the range of -2 to 2. The skewness value of the system security indicator (K), for example, K1 is -0.646, K2 is -0.373, and K3 is – 0.455.
All skewness values on these indicators are in the range of -2 to 2, so it can be concluded that the data is standard. To find the maximum value of sample data in scientific research, you can use SPSS, MS Excel, or other software.
What is Kurtosis?
In statistics, kurtosis is defined as a parameter of the relative sharpness of the peaks of a probability distribution curve. This ensures the way observations are grouped around a distribution center.
It is used to show the flatness or height of the frequency distribution curve and measure the tails or outliers of the distribution.
Positive kurtosis indicates that the distribution is more peaked than the normal distribution. In contrast, negative kurtosis indicates that the distribution is less peaked than the normal distribution.
Types of kurtosis in terms of size distribution are divided into three types: Leptokurtic, Mesokurtic and Platykurtic. The difference is that leptokurtic show kurtosis leading to sharp peaks with fat tails, and are less variable.
Mesokurtic shows kurtosis conditions that are peaking. Finally, there is the platykurtic, which shows the flattest peaks and is very spread out.
Kurtosis Criteria
The degree of sharpness of a curve (kurtosis) is a measure to determine the type of curve (tapered, regular, or flat). The kurtosis (height of the curve) in the frequency distribution is divided into three parts, namely (1) leptokurtic (very sharp), mesokurtis (moderately strong), and platykurtis (flat curve).
The criteria for knowing the distribution model of the kurtosis coefficient are as follows:
- If the coefficient is less than 0.263, then the distribution is platykurtic.
- If the kurtosis coefficient equals 0.263, then the distribution is mesokurtic.
- If the kurtosis coefficient is more than 0.263, then the distribution is leptokurtic.
The Difference between Kurtosis and Skewness
Both skewness and kurtosis are two things that are important to note, especially in the interpretation of descriptive statistics. The difference between skewness and kurtosis lies in the size of the former.
From the size, skewness shows the imbalance in the distribution or distribution of data. While kurtosis describes the level of deadlock in a data distribution.
Skewness alludes to the tendency of the distribution, which determines the symmetry of the mean. While kurtosis focuses more on the size of the sharpness of each curve. Especially in the frequency distribution.