How to find Average of Numbers quickly

It is not that difficult to find the average of numbers.
For most of the candidates who are preparing for competitive exams like SSC, IBPS etc. it can take some time to solve average questions asked in the SSC exams. But what if we know a shortcut method to find the average of numbers, it will not only let us solve the questions quickly but also save our time in the exam and time is precious in competitive exams. So to help you, here we are sharing with you some of the good shortcut tricks to find the average of numbers quickly.
The basic method of finding average of numbers quickly is


Average of numbers= sum of numbers/total No. of numbers
Or you can use the below formula
Average= (sum of 1st  term+sum of last term)/2
Suppose you are given a question as given below:
Find the average of 5,7,9,11,13?
Sol. Whenever you are given a question like the one above:
Here is a very simple trick for this type of questions.
In this type of questions, first look for the difference of numbers. Since the difference is constant throughout i.e. 2. And given numbers are odd in numbers i.e. total 5 types of numbers.
Then in this type of questions, the answer is always the middle term i.e. 9 (in above question).
But if the numbers were given even in numbers means there are six numbers like 5, 7, 9 , 11, 13,15. Then the answer is always sum of middle terms or sum of opposite terms divided by 2 i.e. (5+15)/2 or (7+13)/2 or (9+11)/2. The answer is always same. In the above case the average will be 10.
Suppose you are given a question like the one given below:
A batsman in his 10th innings makes a score of 75 and thereby increases his average by 5. What is his average after 10 innings?
Here is the solution:
Let his average after 10th innings be x, then
Total score after 10th innings= 9x + 75 = 10 (x + 5)
So x = 75 – 50 = 25
So his average after 10 innings = x + 5
= 25 + 5 = 30
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