Formulas To Find Averages
Formulas to Calculate Mathematics Averages:-
General Definition Averages:
An average is defined as the sum of n different units divided by n numbers of the units.
What will be the average weight of three boy, respective weight are 46,54,52 ?
Solution– (sum of numbers/ total numbers)
46+54+53 = 153/3
Basic Averages Formulas:
Mathematically, it is defined as the ratio of summation of all the numbers to the number of units present in the list.
|Average =||x1 + x2 + x3 + x4 +………… xn|
|Average =||Sum of Numbers|
|Number of Units|
Average Speed and Velocity Formula:
- Average Speed : It can be defined as total distance travelled by a body in definite interval of time.
Average speed is calculated using the below formula
Average Speed = Total Distance Total Time
Also , Formula to calculate Average speed when X travels at speed ‘a’ and ‘b’ for the same amount of time is
Average Speed = a + b 2
- Average Velocity :It can be defined as total displacement divided by total time.
We calculate Average Velocity using the below formula :
Average Velocity = Displacement Total Time
Formula of Averages Related to Numbers:
- Average of ‘n’ consecutive Natural Numbers
n +1 2
- Average of the square of consecutive n natural numbers
|(n +1)(2n +1)|
- Average of cubes of consecutive n natural numbers
n(n +1)2 4
- Average of n consecutive even numbers = (n+1)
- Average of consecutive even numbers till n
n + 1 2
- Average of n consecutive odd numbers = n
- Average of consecutive odd numbers till n
n +1 2
- Sum of 1st n even consecutive natural numbers is n(n + 1)
- Sum of 1st n odd consecutive natural numbers is n2