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Averages: Concept, Formulae & Shortcuts

29-NOV-2017 12:46

     

    ‘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:

    Average Formula

    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.

                           Average Example

                           So, Average of First 10 Prime numbers is 12.90.

     

    Tricks to solve problems based on average speed

    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 -

     Average Speed

    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 Speed

    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)

    Learn the concept and formulas for Ratio & Proportion

    WEIGHTED AVERAGE

    Weighted average is calculated with the following formula:

    Weighted Average

    Where, w is the number of occurrences of quantity x.

     

    BASIC FORMULAS

    Below are some basic formulas to remember for solving problems based on the concept of averages:

    Average Formulas

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