An average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. For example, the average of 2,3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4. It is also termed as mean of the given values in statistics. Learn to calculate average value here.
The average formula has many applications both in real-life. Suppose if we have to find the average age of men or women in a group or average male height in India, then we calculate it by adding all the values and dividing it by the number of values. Below is the formula to evaluate the average of given set of numbers.
The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. It can be expressed as:
Average = Sum of Values/ Number of values
Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:
Average = (x1+x2+x3+…+xn)/n
The Arithmetic mean is the most common type of Average. If n numbers are given, each number denoted by ai(where i = 1,2, …, n), the arithmetic mean is the sum of the as divided by n, then:
- n is the number of observation
- i represent index of summation
- and ai = data value for the given index
Average of Negative Numbers
If there are negative numbers present in the list, then also the process or formula to find out the average is the same. Let’s understand this with an example.
Example: Find the average of 3, −7, 6, 12, −2
Solution:- The sum of these numbers
= 3 + (-7) + 6 + 12 + (-2)
= 3 – 7 + 6 + 12 – 2
Total Units = 5
Hence, average = 12/5 = 2.4
How does this whole idea of average or mean works? Average helps you to calculate on how to make all the units present in a list equal.
1) Find the average of 2, 4 , 6, 8.
Add the numbers = 2 + 4 + 6 + 8 = 20
Total Units = 4
Hence, average = 20/4 =5
2) Find the average of 6, 13, 17, 21, 23
Add the numbers = 6 + 13 + 17 + 21 = 60
Total Units = 5
Hence, average = 60/5 =12
3) If the age of 9 students in a team is 12, 13, 11, 12, 13, 12, 11, 12, 12. Then find the average age of students in the team.
Solution: Given, the age of students are 12, 13, 11, 12, 13, 12, 11, 12, 12.
Average = Sum of ages of all the students/Total number of students
A = (12+13+11+12+13+12+11+12+12)/9
A = 108/9
A = 12
Hence, the average age of students in a team is 12 years.
4) If the heights of males in a group are 5.5, 5.3, 5.7, 5.9, 6, 5.10, 5.8, 5.6, 5.4, 6. Then find the average height.
Solution: Given the height of males: 5.5, 5.3, 5.7, 5.9, 6, 5.10, 5.8, 5.6, 5.4 and 6
Average = Sum of heights of males/total number of males
A = (5.5+5.3+5.7+5.9+6+5.10+5.8+5.6+5.4+6)/10
A = 56.3/10
A = 5.63
By closely analysing these examples, one can observe that the average of a certain list of numbers is the central value of the set. Thus, Average or mean is a quantity intermediate of a set of quantities. In Mathematics, this is also called Average Mean.