I want arthamatic mean concept for competitive exams
Answers
Answer:
Arithmetic mean formula
Mathematically, Arithmetic Mean= average = Sum of terms/ No. of terms.
Properties of average
When the difference between all the items is same (and the number of terms is odd), then the average is equal to the middle term. The average of the first and last term would also be the average of all the terms of the sequence.
If x is added to all the items, then the average increases by x.
If x is subtracted from all the items, then the average decreases by x.
If every item is multiplied by x, then the average also gets multiplied by x.
If every item is divided by x, then the average also gets divided by x.
Solved problems
Example 1: Find the arithmetic mean of first five prime numbers.
Solution: First five prime numbers are 2, 3, 5, 7 and 11. The mean or the average formula is = Sum/no. = (2 + 3 + 5 + 7 +11)/5 = 5.6.
Example 2: Find the average of 56, 41, 59, 52, 42 and 44.
Solution: If the given items are very close to each other, a shortcut may be used instead of applying the average formula. Assume that the average is 50, as the terms are around 50 only. Now calculating the difference of all items with 50, you are getting + 6, - 9, +9, + 2, - 8, - 6. Now, if you add these numbers, the result comes out to be - 6. That implies this - 6 will be equally distributed among all the terms and every term will be reduced by - 6/6 = - 1 i.e. average will be reduced by 1. Thus the real average will be 50 - 1 = 49.