* Average *
An average is the result that we get when we add two or more numbers together and divide the total by the number of numbers we added together.
* How do we find the average?
To find the average, first find the sum of all the quantities and then divide it by the total number of quantities. The quotient is called the average of the quantities given.
* Average =
sum of quantities ÷ number of quantities.
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Example 1:
* Find the average of 90 and 110.
sum of quantities.
= 90 + 110 = 200
number of quantities = 2.
Average = ?
(sum of quantities ÷ number of quantities.)
= 200 ÷ 2 = 100
Average = 100 And.
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Example 2 :
* Find the average of first 4 multiples of 8.
First 4 multiples of 8 are
8, 16, 24, 32.
sum of quantities.
= 8+16+24+32 = 80
number of quantities = 4.
Average = ?
(sum of quantities ÷ number of quantities.)
= 80 ÷ 4 = 20
Average = 20 Ans.
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Example 3 :
* The average of 3 numbers is 15 and two numbers are 20 and 15. Find out the third number.
The average of number = 15
Sum of number = 15×3 = 45
Sum of two given numbers
= 20+15 = 35.
Hence, the third number
= 45 - 35 = 10 Ans.
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Example 4 :
Find the average of 1/3, 1/4, 1/6.
Sum of number =
1/3 + 1/4 + 1/6 = 4+3+2/12
= 9/12
Average of number = 9/12÷3
1/12 ÷ 1/3 = 1/4 Ans.
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* Important rules for calculating the average of even and odd numbers.
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* Trick: (A)
[ Average of first "n" odd numbers = n ]
The average of the first 5/6/7/8/9/10...... odd numbers
=Answer will be 5/6/7/8/9/10......
Shortcut method ( = n)
for odd numbers.
Average of first 2 odd numbers
= 2 Ans.
Average of first 3 odd numbers
= 3 Ans.
Average of first 4 odd numbers
= 4 Ans.
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* By rule:
* What is the average of the first 5 odd numbers?
The first 5 are odd numbers.
1, 3, 5, 7, 9 .
sum of quantities.
= 1+3+5+7+9 = 25
number of quantities = 5.
Average = ?
(sum of quantities ÷ number of quantities.)
= 25 ÷ 5 = 5
Average = 5 Ans.
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* Trick: (B)
[ Average of first n even numbers = n + 1]
The average of the first 5/6/7/8/9/10...... even numbers
=Answer will be 5+1= 6 / 6+1=7/ 7+1=8 / 8+1=9 / 9+1=10 / 10+1=11.........
Shortcut method ( n+1)
for even numbers.
Average of first 2 even numbers
= 2+1 = 3 Ans.
Average of first 3 even numbers
= 3+1 = 4 Ans.
Average of first 4 even numbers
= 4+1 = 5 Ans.
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* By rule:
The first 5 are even numbers.
2, 4, 6, 8, 10 .
sum of quantities.
= 2+4+6+8+10 = 30
number of quantities = 5.
Average = ?
(sum of quantities ÷ number of quantities.)
= 30 ÷ 5 = 6
Average = 6 Ans.
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Obviously the average of the first
'n' even number = n + 1
Hence, average of first 5000 even number = 5000 + 1 = 5001 Answer
Alternative method
[Sum can be calculated by adding the given numbers in a simple way. But if the given numbers are in a list and if they form a range, they can be added easily with the help of a formula.]
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