Average
1 What is Average?
1 What is Average?
A
calculated "central" value of a set of numbers.
Average = Sum of Observation
Number of Observation
When we cross multiply
Sum of
observation = Average of Observations * Number of observation
2 In case of Average speed, the formula
will change
What is Average Speed?
Average Speed is the total distance traveled by an objects divided by total time taken.
If distance and time are not mentioned rather the speeds are given, then;
Suppose a man covers a certain distance at X km/h and an equal distance at Y km/h
Then the Average Speed during the whole
journey is
Average
Speed = 2XY
X+Y
When there are three speeds X km/h, Y km/h
& Z km/h
Average
Speed = 3XYZ
XY+YZ +ZX
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3. If the
average of n1 items is p1 and the average of n2 items is p2 then
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The average of
total items will be
n1p1 + n2p2
n1 +n2
Example: There
are 60 students in a class. Out of which 40 are boys and 20 are girls. If the average
age of boys is 15 years and that of girls is 16 years then find the average age
of the class.
40*15 + 20*16.
60
Ans. 15.33 years
4. When we have
to find the average of consecutive
odd numbers
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Then,
Case 1: - When the number of observation is Even
Example: - 11, 13, 15, 17 (here the number of observation is 4, even)
Divide the numbers equally in two parts
11, 13 …….15, 17
The number between middle two terms is average, i.e. 14 in this case.
Alternative method: Sum of extremes divided by 2
Here 11+17 = 14
2
Case 2: - When the number of observation is Odd
Example: - 163, 165, 167,169,171 (here the number of observation is 5, Odd)
Here the middle term is the average i.e. 167
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5. Average of
consecutive first n natural numbers is
n+1 .
2
Average of first
20 natural numbers is 20+1 divided by 2 i.e. 10.5.
Sum of first consecutive n natural numbers is
n(n+1) .
2
As
Sum of Observations = Average of Observations * Number of observation
6. Average of consecutive first n natural even numbers is n+1.
Example: - Average of consecutive first 5 natural even numbers is 5+1 =6
Long method 2+4+6+8+10
5
30/5= 6
Average of consecutive first n natural odd numbers is n.
Example: - Average of consecutive first 5 natural odd numbers is 5
Long method 1+3+5+7+9
5
25/5= 5
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Average of n multiples of p will be
p(n+1) .
2
5(3+1)/2 =
Long method 5+10+15
2
Ans. 10
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