‘Average’ is the most basic concept of Arithmetic in Quantitative Aptitude section. In competitive exams you are likely to find tricky questions based on this topic as the concept of averages is quite easy and known to all.
The term ‘Average’ refers to the sum of all observations divided by the total number of observations. Average is used quite regular in our day to day life. For example to calculate the average marks of the students, average height of a particular group, etc. The term average is also referred to as ‘Mean’. Basic formula to calculate the average is as follows:
Example: What is the average of first 10 Prime numbers?
Solution: First 10 Prime numbers are 2,3,5,7,11,13,17, 19, 23 and 29.
So, Average of First 10 Prime numbers is 12.90.
If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by -
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 -
When a person leaves the group and another person joins the group in place of that person then:
Age of new person = Age of separated person + (Increase in average × total number of persons)
Age of new person = Age of separated person - (Decrease in average × total number of persons)
Similarly, when a person joins the group, then:
Age of new member = Previous average + (Increase in average × Number of members including new member)
Age of new member = Previous average - (Decrease in average × Number of members including new member)
Weighted average is calculated with the following formula:
Where, w is the number of occurrences of quantity x.
Below are some basic formulas to remember for solving problems based on the concept of averages: