What is Average?
The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.
Formula
Average: = (Sum of observations / Number of observations)
Average: = (Sum of observations / Number of observations)
Average speed
- Average speed=total distance/total time taken.
- If a moving object covers a certain distance with a speed of x km/hr and again covers same distance with a speed of ykm/hr, then average speed is
- If a moving object covers a certain distance with a speed of x km/hr and again covers same distance with a speed of ykm/hr and again with zkm/hr,then average speed is
- If a person covers A km at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is-
Average:Removal and Insertions of new term
- When a person leaves the group and another person joins the group in place of that person then-If the average age is increased
Age of new person = Age of separated person + (Increase in average × total number of persons)
If the average age is decreased,
Age of new person = Age of separated person - (Decrease in average × total number of persons) - When a person joins the group. In case of increase in average
Age of new member = Previous average + (Increase in average × Number of members including new member) - In case of decrease in average
Age of new member = Previous average - (Decrease in average × Number of members including new member)
Average of first n natural numbers
- Sum of first n natural numbers,
- Average = Sum of first n natural numbers/n,
Average of an arithmetic progression
An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For example 3,7,11,15……is an arithmetic progression with common difference of 4
Generally we can write an AP as a, a+d,a+2d,a+3d………,a+nd
‘a’ is the first term and ‘d’ is the common difference, ’n’ is the total no of terms.
nth term of A.P is given by
This sum can be found quickly by taking the number n of terms being added ,multiplying by the sum of the first and last number in the progression, and dividing by 2:
Therefore Average of an A.P is
For example 3,7,11,15……is an arithmetic progression with common difference of 4
Generally we can write an AP as a, a+d,a+2d,a+3d………,a+nd
‘a’ is the first term and ‘d’ is the common difference, ’n’ is the total no of terms.
nth term of A.P is given by
This sum can be found quickly by taking the number n of terms being added ,multiplying by the sum of the first and last number in the progression, and dividing by 2:
Therefore Average of an A.P is
