Basic Formulas of Average
The following are the formulas relevant to Average questions:
S.No | To Calculate | Formulas |
---|---|---|
1 |
Average of first n natural numbers |
$\left(a+1\right)/2$ |
2 |
Average of squares of first n natural numbers |
$\left(n+1\right)\left(2n+1\right)/6$ |
3 |
Average of cubes of first n natural numbers |
$n{\left(n+1\right)}^{\wedge}2/4$ |
4 |
Average of first n even numbers |
$\left(n+1\right)$ |
5 |
Average of squares of first n even numbers |
$2\left(n+1\right)\left(2n+1\right)/3$ |
6 |
Average of cube of first n even numbers |
$2n{\left(n+1\right)}^{\wedge}2$ |
7 |
Average of first n odd numbers |
n |
8 |
Average of squares of first n odd numbers |
$\left(2n+1\right)\left(2n-1\right)/3$ |
9 |
Average of cube of first n odd numbers |
$n\left(2{n}^{2}-1\right)$ |
10 |
Average (If the value of each number is increased/decreased/multiplied/divided by the same value ‘a’) |
Then the average of all numbers will also be increased/decreased/multiplied/divided by the same value ‘a’. |
11 |
New Average (Change in average due to insertion and deletion of values) |
Old Average ±(Deviation / number of people) |
12 |
Average Speed |
Total distance covered ÷ Total time taken |
Some Quick Tricks on Average Formulas
The Average age of a group of boys is given. If the new Average age after a boy joins the group is also provided, the age of the new boy is given by;
Age of new boy = New Average + (Number of boys initially ∗ Increase in Average)
The Average weight of a group of persons is given. If we replace a person in the group with another person and the new Average is increased,
The weight of the new person = weight of the removed person +( Number of persons ∗ Increase in Average)
Quick Tip: Do you know? You can learn Average formulas quickly if you first understand the fundamental concepts of Average.
FAQsFAQs
How do you benefit from learning Average formulas?
One of the significant benefits of understanding formulas is the capability to quickly and accurately address simple formula-based Average questions.
How to remember Average formulas for a longer time?
Following are the techniques you can use to memorise Average formulas:
For a start, you can start understanding the concepts of the Average. It will help you find out why a formula is used.
Keep a separate piece of paper and write down each formula on the Average topic you need to memorise.
Write down and examine each Average formula, but this time with intervals. Write the equation, then take a 2-minute break to think about it before writing it again.
Your memory is more likely to associate with the formula you want to remember if you use it more often. Solve the problems employing the formula.
Visualise and repeat out loud the formula occasionally. Create Average formulas flashcards to help with this. You can also use these flashcards while practicing the Average questions.
The formula should be written down and posted somewhere you will see daily. They'll be subconsciously imprinted into your memory.
How conceptual understanding of Average topic helps in remembering its formulas?
Conceptual understanding will help you to make sense of the Average formulas. Conceptual understanding is concentrated on describing why things happen as opposed to how to make them happen. They help you understand the true motive for employing the Average formulas.