**Average**

**Important Formulas - Average**

1. Average = Sum of Observation / Number of observation

2. Average Speed : If a car covers a certain distance at x kmph and an equal distance

at y kmph. Then,the average speed of the whole journey = 2XY / X+Y kmph.

**Example 1**: Weight of student = 40,50,60,65,55,45 kg. What is average age of class

of student

**Solution**: (40+50+60+65+55+45)/6 = 52.5

**Example 2**: Suppose there is no. of people is 9 and the old average was 80

and the new guys comes at 90 kg. What is new average going to be ?

**Solution**: Remember in the beginning when we decided to find the average, first we find the

sum and Divided by the no of people.

the old avg of 9 people = 80kg

new total 10 people. So 80 + 10 kg, so individually increase 1 kg.

N =10 so individually 80 + 1 = 81 avg= 81

**Weighted Average**: (W1X1 + W2X2 + --------- + WnXn) / (W1 + W2 + ------ + Wn)

**Weighted Average**comes in handy in slightly different ways. Lets say we talk about a

class, where

5 students got 4

6 students got 7

8 students got 10 on10

**Solution**: we know that, 5 student got 4 = 5 × 4 , that is the weight that we assign to mark 4 as 5 student got that., similarly other also,

So the weighted Average = (5*4 + 6*7 + 8*10) / 5+6+7 = (20+42+80)/19𝟖= 7.47

Assumed Average : Another method is used for calculating the averages is the

Assumed Average Method. For the assumed average method we need to

understand Deviation.

The sum of Deviation (D) of each element with respect to the average is 0.

D = (X1-Xavg)+ (X2-Xavg)+(X3-Xavg)......+ (Xn-Xavg) = 0

Xavg = Xassumed avg + (Deviation / No. of Element)

Lets take some values 1,3,5,6 and Average = 3.75

Then the Deviation of 1st values is 1 - 3.75 = - 2.75

Deviation of 2nd values is 3- 3.75 = 0.75

Deviation of 3rd values is 5 - 3.75 = 1.25

Deviation of Final values is 6 - 3.75 = 2.55

This are the individual Deviation. The Deviation as nothing else but the difference of

any particular value from the Average.

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