What are some Measures of Central Tendency besides Mean, Median, and Mode?
An Introduction
A single number that seeks to characterize a set of data by pinpointing the central location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean and mean calculator online (sometimes known as the average), but there are some additional central tendency measures methods, including the mid-point, Geometric mean, Truncated mean, or trimmed mean.
Truncated mean or trimmed mean
By eliminating certain inconsistent data, a trimmed mean is a technique for determining an average value that is more realistic. With this approach, before computing the mean, a fraction of the greatest and lowest values are removed from both extremes. The mean value is more trustworthy as a result of this pre-calculation removal.
In statistics, a trimmed mean is a statistical term for a shortened portion of the arithmetic mean. Consequently, it is often referred to as the shortened mean. The greatest and lowest values are removed from the observation series by subtracting a certain percentage from both ends. The observations in this series are listed in increasing order. There are three trim percentages that are frequently used: 5 percent, 10 percent, and 20 percent. Also, you can use the trimmed mean calculator with steps to find out the central tendency.
Many studies use the shortened mean to reduce sampling fluctuations. Using this strategy, it is possible to prevent the dominance of extreme data points in the Olympics. The shortened mean aids in removing large price swings when computing inflation rates.
Formula:
μ = Sum of your number Set / Total Numbers Entered
Mid-Range or Mid-Extreme
In simple words, the midpoint of any data collection is the average or mean of the data. A statistical tool known as a midrange is also referred to as the statistic’s measure of center. As a measure of central tendency, medium, average, mode, and range are also recognized in addition to the midrange formula means.
The value between the highest value and the lowest value is the data set’s midpoint. Following the addition of the lowest and highest values in the data set, the value is divided by two in order to get the data set’s middle.
In this post, we’ll try to grasp how the Midrange formula functions and the reasoning behind it. as well as its application and importance. However, some statisticians advise that we present the data in ascending and descending order in order to determine the midpoint of the data set. It is not required to organize the current data in ascending and descending order since we are selecting the lowest and highest value of the data and the midpoint of the data set.
Formula:
Mid-Range = (Max (x) + Min (x) / 2)
Geometric Mean
The Geometric Mean (GM) is the average value or mean that, by taking the product of a set of numbers’ values as its root, indicates the collection’s central tendency. In essence, where n is the total number of values, we multiply all ‘n’ values together and subtract the nth root of the numbers.
Formula:
GM = √x₁ · x₂ · … · xₙ
Geometric Mean Definition
The average value or mean that, by computing the product of the values of the set of numbers, represents the central tendency of the numbers is known as the Geometric Mean (GM) in mathematics. Basically, we add the numbers and use the sum of the numbers to determine the n-root of the numbers, where n is the total quantity of data. The geometric mean, for instance, is (31) = 3 = 1.732 for a given pair of integers, such as 3 and 1.
In other terms, the geometric mean is the product of n numbers divided by the nth root. The geometric mean differs from the arithmetic mean, as is stated. As the result in arithmetic mean, the data values added in before the start are divided by all numbers. However, while calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root from the values, to confirm that, if there are two data points, the cube root if there are three, fourth, and four roots, and so on.
Formula:
Μ = [(1 + R1) (1 + R2)…(1 + Rn)]1/n−1
