Important Formulas: Average | Quantitative for GMAT PDF Download

Average

An average is defined as the sum of n different units divided by n numbers of the units.

Example:- What will be the average weight of three boy, respective weight are 46,54,53?
Sol:

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.

or

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

Case 1:
When one travels at speed ‘a’ for half the time and speed ‘b’ for other half of the time. Then, average speed is the arithmetic mean of the two speeds.

Case 2:
When one travels at speed ‘a’ for half of the distance and speed ‘b’ for other half of the distance.Then, average speed is the harmonic mean of the two speeds.

Case 3:

When one travels at speed a for one-third of the distance, at speed b for another one-third of the distance and speed c for rest of the one-third of the distance
or

Average Velocity: It can be defined as total displacement divided by total time. We calculate Average Velocity using the below formula

Formula of Averages Related to Numbers

• Average  of ‘n’ consecutive Natural Numbers = (n+1)/2
• Average of the square of consecutive n natural numbers =
• Average of cubes of consecutive n natural numbers =
• Average of n consecutive even numbers = (n+1)
• Average of consecutive even numbers till n =
• Average of n consecutive odd numbers = n
• Average of consecutive odd numbers till n =
• Sum of 1st n even consecutive natural numbers is =  n(n + 1)
• Sum of 1st n odd consecutive natural numbers is = n²

Example 1 : The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Sol:
Average of 10 numbers = 23
Sum/Total numbers = 23
Sum/10 = 23
Sum of the 10 numbers = 230
If each number is increased by 4, the total increase = 4 x 10 = 40
New sum = 230 + 40 = 270
Therefore, the new average = 270/10 = 27

Example 2: The average weight of a group of seven boys is 56 kg. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy.
Sol: 
Average weight of 7 boys = 56 kg.
Total weight of 7 boys = (56 × 7) kg = 392 kg.
Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg = 338 kg.

Weight of the 7th boy = (total weight of 7 boys) – (total weight of 6 boys) = (392 – 338) kg

= 54 kg.
Therefore, the weight of the seventh boy is 54 kg.