Average
Average or mean
Number which show the central value of a set of given numbers.
Formula
Sum of observations
-----------------------------------
Number of observations
1) Rule :
If each one of some given numbers is multiplied by k, then their average or mean is multiplied by k._
2) Rule:
If each one of some given numbers is increased by k, then their average or mean is increased by k.
3) Rule :
A man cover a distance from A to B at u km/hr and returns back to A at uniform speed of v km/hr, then the speed during the whole distance 2uv/(u+v) km/hr.
Example
1) Find the average of first 4 prime numbers.
Solution:
2+3+5+7
= -----------------------
4
= 17/4 = 4.25
2)Find the average of first 18 multiples of 6 .
Solution:
Sum of multiples of 6
Average = ------------------------------------------
Number of multiple of 6
6(1+2+3+.............+18)
= ----------------------------------------------
18
= 57
3) Aman covers a distance from a town A to B on scooter at 30 km per hour and rides back from B to A at 20 km per hour. Find his average speed during the whole journey .
Solution :
Average speed = 2uv/(u + v)km/hr
=2X30X20/(30+20) km/hr.
= 24km/hr
4)The average temperature for Monday, Tuesday and Wednesday was 40 degree C . The average for Tuesday,Wednesday and Thursday was 41 degree C. If the temperature on Thursday be 42 degree C, Find the temperature on Monday.
Solution:
(M+T+W) = (3X40)
= 120
(T+W+Th) = (3X41)
= 123
On subtraction
Th -M =3
Therefore M = (Th -3 ) = (42 -3 ) = 39
Hence, the temperature on Monday was 39 degree C.
5) The average of 11 results is 50. If the average of first six results is 49 and that of last six is 52, Find the sixth result.
Solution:
Sum of 11 results = ( 11 X 50 )
= 550
Sum of first 6 results = 6 X 49
= 294
Sum of last 6 results = 6 X 52
= 312
therefore 6th result = 294 +312 - 550 = 56
Exercise
1) A motorist covered the first 20 km of his journey in 30 minutes and the remaining 29 km in 40 minutes. His average speed in km/hr is :
a)41 b)42 c)49 d)59
2) The mean of 19 observations is 4. If one more observation of 24 is added to the data, the new mean will be :
a)4 b)5 c)6 d)7
3) If the mean of 4 observations is 20 and when a constant C is added to each observation, the mean becomes 22, the value of C is :
a)-2 b)2 c)4 d)6
4)The average weight of a group of 20 boys was calculated to be 89.4 kg and it was later discovered that one weight was misread as 78 kg instead of the correct one of 87 kg. The correct average weight is :
a)88.95 kg b)89.25 kg c)89.55 kg d)89.85 kg
5)The A.M. of the price per kg of rice at 10 different places was Rs. 4.85. After a week, the price per kg was increased by 20 paise at 3 places and decreased by 10 paise at one place. The new average of price per kg is :
a)Rs 4.88 b)Rs 4.86 c)Rs.4.90 d)Rs 5.35
Answer
1) b 2) a 3) b 4) d 5) c
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