# Important Formulas - Average - Tricks & Shortcuts

**1) Average:**

**Average = (Sum of observations/Number of observations)**

**Example:**

If a teacher tutored five students and they subsequently scored 96, 94, 92, 87, and 81, what was the average score of the students whom the teacher tutored?

N = 5 since there are 5 students(Number of Observations)

S = 96 + 94 + 92 + 87 + 81 = 450(Sum of Observations)

**Average**= S/N = 450/5 = 90

**2) Average Speed:**

Suppose a man covers a certain distance at

**x kmph**and an equal distance at

**y kmph**.

Then, the average speed druing the whole journey is

**[(2xy)/(x + y)] kmph**.

3) Average of consecutive

**first n natural numbers**is

**= (n+1)/2**

4) Average of

**first n natural EVEN number**s is

**= (n+1)**

5) Average of

**natural even numbers**up to n is

**= (n/2)+1**

6) Average of

**first n natural odd numbers**is =

**n**

7) Average of

**natural odd numbers**up to n is

**= (n+1)/2**

8) Average of

**n multiples of p**will be =

**{p(n+1)}/2**

9) If a person covers a certain distance at a speed of

**x km/h**and

**y km/h**and

**z km/h**respectively, then his average speed will be

**= (3xyz)/(xy+yz+zx)**

10) If the average of

**n1 items is p1**and average of

**n2 items is p2**then the average of total items

**(n1+n2) will be = (n1p1+n2p2)/(n1+n2)**

11) The average of ages of x members of a family is y years. Now if a new member joins the family, then the new average of ages of all the members is z. Then the age of new member will be =

**[z-x(z-y)] years**

12) The average of ages of x members of a family is y years. Now if a member leaves the family, then the new average of ages of all the members is z. then the age of that member will be

**= [z+x(y-z)] years**

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Important Formulas - Average - Tricks & Shortcuts
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