amitkmr988

· 04 Jan 2022

Follow Following

How to find mean?

In a common term, mean of a data is that number that when sum by itself will give the same result as the sum of the data. For instance, if the mean of 3, 5,8, That is( 3 + 5 + 8)= 16 /3=5.333, therefore, 5.333 +5.333+5.333 = 16 Mean is one of the important and most commonly used measures of central tendency. There are several types of means in mathematics. In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection÷ of data divided by the total number of values in the data. In other words, we can simply add all the values in a data set and divide it by the total number of values to calculate mean. However, the general method and formulas vary depending upon the type of data given, grouped data, or ungrouped data.

Grouped data is the data set formed by aggregating individual observations of a variable into different groups, while ungrouped data is a random set of observations. Let us understand the different mean formulas and methods to find the mean of the given set of observations using examples.

What is Mean in Statistics?
Mean is a statistical concept that carries a major significance in finance and is used in various financial fields and business valuation. Mean, median, and mode are the three statistical measures of the central tendency of data.

Mean Definition

The mean is the average or a calculated central value of a set of numbers and is used to measure the central tendency of the data. Central tendency is the statistical measure that recognizes the entire set of data or distribution through a single value. It provides an exact description of the whole data. In statistics, the mean can also be defined as the sum of all observations to the total number of observations.

Types of Mean in Math

There are different types of mean in mathematics, which are arithmetic mean, weighted mean, geometric mean (GM), and harmonic mean (HM). If mentioned without an adjective (as mean), mean generally refers to the arithmetic mean in statistics. Some of the types of the mean are explained in brief as given below,
•    Arithmetic Mean
•    Weighted Mean
•    Geometric Mean  •
•    Harmonic Mean  

Arithmetic Mean

Arithmetic mean is often referred to as the mean or arithmetic average, and is calculated by adding all the numbers in a given data set and then dividing it by the total number of items within that set. The general formula to find the arithmetic mean is given as,
x̄ = Σfi/N

Where:

x̄ = the mean value of the set of given data.
f = frequency of the individual data
N = sum of frequencies
Calculating Mean.
In statistics, mean of a group data and mean of an ungrouped data are calculated differently

Formula for Mean of ungrouped data

The mean of ungrouped data is calculated using the formula below
Mean = (Sum of observation) ÷ (Total number of observation)
Formula for mean of grouped data
The mean formula for a grouped data is given as
x̄ = Σfx/Σf
x̄ = the mean value of the set of given data.
f = frequency of each class
x = mid-interval value of each class
Work examples
1. Find the mean of the following data
1,2,3,4,5,6,7
Solution
Mean = (sum of observation)/ (total number of observation
Mean = (1+2+3+4+5+6+7)/7
Mean = 28/7 = 4
Example 2.
Assuming the height of five students in a class is 161, 120, 140, 130, and 150. Find the mean of their heights.

Solution

Mean = (sum of the observation)/(number of observation)
Mean = (161 + 120 + 140 + 130 +150)/ 5
Mean = 701/5
Mean = 140.5
#mean #how #find #math