The state of getting dispersed or spread is known as dispersion. In statistics, dispersion means the extent to which a numerical value varies from an average value. In simpler terms, it is the calculation of the area to which the values differ from the average. But how do you calculate dispersions? Well, there are several methods to calculate the extent of dispersion. These methods are known as the measures of dispersion. Among these methods, there are two widely used measures of dispersion. But what is the importance of measures of dispersion or what is the best measure of dispersion? Read the article to know more about these methods.
1. What are the Measures of Dispersion?
A measure of dispersion indicates data scattering. It explains the differences in data, providing a detailed picture of their distribution. The extent of dispersion illustrates and informs us about a single object’s variance and central value. Measures of dispersion can be calculated with the help of five types of methods. The five types of measures of dispersion are standard deviation, range, mean absolute difference, mean absolute deviation, interquartile change, and average deviation. (See How to find the Common Difference of the Arithmetic Sequence?)
2. Which is the Best Measure of Dispersion?
The best measure of dispersion is the Standard Deviation (SD). Among the two widely used measures of dispersion, this method of dispersion is the spread of data about the mean. The square root of the sum of squared deviations from the mean divided by the number of observations is the Standard Deviation or SD.
3. What are Two widely used Measures of Dispersion?
Among the several methods, the two widely used measures of dispersion are Standard Deviation (SD) and Range. In statistics, the range is the difference between the highest and lowest values for a particular data collection. For instance, if the provided data set is 2, 5, 8, 10, 3, the range is 10 – 2 = 8. As a result, the range may alternatively be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.
The standard deviation is a metric that illustrates how much variation (such as spread, dispersion, and spread) occurs from the mean. The standard deviation represents a typical departure from the mean. It is a common measure of variability since it returns to the data set’s original units of measurement.
4. Why Standard Deviation is the Most Widely Used Measure of Dispersion?
There are two widely used measures of dispersion, the Standard deviation and the Range, the standard deviation is the most widely used and recognized measure of dispersion as it is a metric that displays how much variance there is from the mean. The standard deviation represents a typical departure from the mean. It is a common measure of variability since it returns to the data set’s original units of measurement.
The most generally used metric of dispersion, standard deviation, is based on all data. As a result, even a little change in one number influences the standard deviation. It is origin-independent but not scale-independent. It can also help with some sophisticated statistical difficulties. (See What is the GCF of 24 and 32?)
5. What are the Two Importance of Measures of Dispersion?
Since you know about the two widely used measures of dispersion, note that the fluctuations between the values or to calculate the frequency are read by the measures of dispersion. Standard deviation is the most widely used measure of dispersion. But what is the importance of measures of dispersion? Well, here are two important measures of dispersion:
- To calculate the reliability of an average: When the dispersion is relatively small, the typical value of an average is close to the individual value and hence, the estimation of the average is good and reliable. However, when the dispersion is large, the average, being not so typical gives an unreliable estimate.
- Comparison of two or more series as per their variability: It is a study of the variation. In other words, it is the measurement of uniformity or consistency. If the variation ranges with a higher difference, then the uniformity or consistency would be little, and if the variation ranges with a lower difference the uniformity or consistency would be high.
6. What is Absolute and Relative Measure of Dispersion?
The absolute measure of dispersion carries the same value or unit as the original data. The absolute measure of the dispersion method expresses differences in average deviations observed such as the Standard Deviation or the mean deviation which is the best measure of dispersion. Here are the following types of absolute deviation:
- Range: It is the difference between the maximum and the minimum value that is given in a data set. For example, a data set of 1,2,3,4 has a range of 4-1.
- Variance: To calculate the variance, subtract the mean from each data point in the set, square each one, add each square, and then divide the total number of values into the data set. Variance (σ2) = (∑(X−μ)2)/N
- Standard Deviation or SD: Standard deviation is the square root of the variance.
- Quartiles and Quartile deviation: The values that divide the list of numbers into quarters are known as Quartiles. The measurement of half the distance between the third and the first quartile is known as the Quartile Deviation.
- Mean and Mean Deviation: The average of the numerical values is known as the Mean. Mean deviation is known as the arithmetic mean of the absolute deviations of the values observed.
The calculation to compare the distribution between two or more given sets is known as the relative measure of dispersion. The measurement is executed without units. The various methods of a relative measure of dispersion are:
- Coefficient of range
- Coefficient of Variation
- Coefficient of Standard Deviation
- Coefficient of Quartile deviation
- Coefficient of Mean Deviation
7. What is the Other Name for Relative Measure of Dispersion?
The other name for a relative measure of dispersion is the coefficient of variation. It is a technique for calculating ratio scales from paired comparisons given by absolute variables. It is used most of the time while measuring central tendency in calculating mean or median, in order to give an overall description of the data set provided. (See What are the Prime Numbers between 20 and 30?)
8. Is Quartile Deviation a Measure of Dispersion?
Yes, quartile deviation is a measure of dispersion as it calculates the spread within which the values or data lie. It is not to be confused with Quartile, as Quartile and Percentiles are not measures of dispersion but is the measurement of the position of a specific data point within a given data set.
9. Is Mode a Measure of Dispersion?
Yes, the mode is a measure of dispersion. The measure of dispersion is the measurement of the spread of data within a provided data set. This measurement method includes mean, median, mode, range, upper and lower qualities, variance, and standard deviation. (See Which Correlation is the Strongest?)
10. What are the Three Most widely used Measures of Central Location?
Besides wondering about the two widely used measures of dispersion, you should know that the three most widely used measures of a central location or central tendency are the mean, median, and mode.
- Mode: The Mode is defined as the most commonly occurring variable in a distribution set. For example, in a set of 21,21,21, 34,32,44,43,43; here 21 is the mode as it occurs most commonly.
- Median: The median is defined as the middle value in a distribution set. To find out the median from a given distribution, it is essential to arrange the distribution in an ascending and descending order.
- Mean: The mean is defined as the sum of each value in a given distribution divided by the number of observations. It is simply referred to as Average.
We may conclude with the fact that measures of a central tendency are not the measurement of dispersion but a part of it. So, what are the two widely used measures of dispersion? The measurement of Dispersion carries various methods such as the standard deviation, variance, coefficients, Quartiles, and their deviation, mean and mean deviation, and various other methods that are described earlier. Generally, Standard Deviation and Range, Quartiles, and Quartile deviation are the most commonly used measures of dispersion.