In mathematics, the three main methods for indicating the average value of a list of numbers are mean, median, and mode. To determine the arithmetic mean, add the numbers together and divide the result by the total number of numbers in the list. This is what most people mean when they say "average." The median is the value in the middle of a list that is ordered from smallest to largest. On the list, the mode value appears the most frequently.
What is Mean?
Mean is one of a data set's central tendencies that is used to represent the average of a data set. It is one of the most basic, yet crucial, tools for determining the 'average' in statistics.
Mean is simply defined as the 'average' of a numerical dataset. It is calculated by adding all of the observations in a data set and then dividing the total number of observations by the total number of observations. Given below are the different types of mean:
Arithmetic Mean
The Arithmetic Mean can be defined as the sum of all observations. In general, if the mean is not preceded by an adjective, it is assumed to be an Arithmetic Mean.
Weighted Mean
The difference between weighted mean and arithmetic mean is that in weighted mean, some values contribute more than others. The weighted mean is useful when one observation is more important than others.
Harmonic Mean
The Harmonic Mean is calculated by dividing the total number of observations by each observation's reciprocal. It is extremely useful in physics and has numerous other applications.
(example- average speed when the duration of several trips is known).
It is given by the formula-
H.M= n/ (1/x1)+(1/x2)+(1/x3)+.....(1/xn)H.M=n(1/x1)+(1/x2)+(1/x3)+.....(1/xn)
Geometric Mean
The Geometric Mean calculates the central tendency by taking the product of the observations rather than the sum of the observations (as in the Arithmetic Mean).
What is Median?
The value of the middlemost observation obtained after arranging the data in ascending or descending order is the median of the data.
Where,
n = Total frequency
F = Cumulative frequency of class before the median class
fm = Frequency of the class median
i = Class width
Lm = Lower boundary of the class median
For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.
What is Mode?
A mode of data is the value that appears the most frequently in the given data, i.e. the most frequent observation.
where,
'L' is the lower limit of the modal class.
'h' is the size of the class interval.
‘fm' is the frequency of the modal class.
'f1' is the frequency of the class preceding the modal class.
'f2' is the frequency of the class succeeding the modal class.