Averages: Concept, Formulae & Shortcuts
‘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.
Tricks to solve problems based on average speed
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 -
Tricks to solve problems based on ages
When a person leaves the group and another person joins the group in place of that person then:
- If the average age is increased, then
Age of new person = Age of separated person + (Increase in average × total number of persons)
- If the average age is decreased, then
Age of new person = Age of separated person - (Decrease in average × total number of persons)
Tricks to solve problems based on calculating members in the group
Similarly, when a person joins the group, then:
- 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)
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: