12. Average

12. Average

Learn and Remember :

1. The average of n numbers is equal to the sum of n numbers, divided by n.

e.g. the average of three numbers 35, 65 and 80

∴= 35 +65 +80/ 180

∴=180/3

∴= 60

2. The average of three consecutive numbers is equal to the middle number.

e.g. the average of 14, 15 and 16 is the number 15.

[Note : The same is true for five, seven, nine, ..., consecutive numbers.]

3. The average of 3 consecutive even numbers, or 3 consecutive odd numbers is equal to their middle number. The same is true for five, seven, nine, ..., consecutive even numbers or consecutive odd numbers.

e.g. (i) The average of the three consecutive even numbers 12, 14 and 16 is equal to their middle number 14.

(ii) The average of the numbers 13, 15, 17, 19 and 21 is equal to their middle number 17.

4. For any three numbers with equal difference between them, the average is equal to the middle number. The same is also true for five, seven, nine, ..., numbers with equal difference.

e.g. the average of the numbers 12, 19 and 26 is the number 19. (The difference between 19 and 12 is 7. Also, the difference between 26 and 19 is 7.).

5. The average of four (or six, eight, ...) odd or even numbers is the average of their middle two numbers.

e.g. (i) The average of 8, 10, 12, 14, 16,18 is the average of 12 and 14.

i.e.  12 +14/2 

∴ = 26/2

∴  = 13.

Note that, if the numbers are even their average is an odd number.

(ii) The average of 13, 15, 17, 19, 21, 23 is the average of 17 and 19.

i.e.  17+19 /2

∴ = 36/2 

∴ =  18.

Note that, if the numbers are odd their average is an even number.

6.The frequency table is used when the numbers whose average is to be found out is very large.

7. Speed = distance ÷ time 

∴ speed is also a type of  average .

8. The average of consecutive  numbers = The first number + The last number/2