Average Maths Short Tricks, Questions with Solutions
Contents
What is average?
The average of a group of set of N number is define as the sum of those numbers divided by N.
Here N is the number of values of observation in a set.
Average = sum of N number/ Number of observations
A=Sum/N or Sum= N*Average
Example: If weight of 4 child are 30, 35 and 25 pounds, then average of the weight of child can be calculated as:
Average= Sum of weight of child/ Number of child
=30+35+25/3
=30
USING AVERAGE TO FIND A NUMBER
Sometimes average will be given and we have to find the missing number in this type of case, they give us.
Average value and the number of observation are given.Except the missing observation.
Example:
If average of 3,4,5 and x is 5, what is the value of x?
We have given , N=4 observation, and average of these observation is 5.
Average= Sum/N
5= (3+4+5+x)/4
20=12+x
x=8
Hence, the missing observation is 8.
AVERAGE IN DIFFERENT CASES:
1. If all the number in a set are the same, then that number is the average of that set.
Example:
Average of set of values 6 ,6 and 6
Also by theory. Average=Sum/N
=6+6+6/3
=6.
2. If the number in a set are not all the same , then the average must be greater than the smallest number and less than the greatest number in that set.
Example:
Average of set values 83,84,87,97,99
Average= Sum/N
=83+84+87+97+99/5
=90
Here 90>83 and 90<99
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SOME IMPORTANT FACT
- If each one of the given number is increased by constant K, then their average is increased by K.
- Average of n consecutive natural = n+1/2.
- Average of squares of n consecutive natural number= (n+1)(2n+1)/6
- Average of cubes of n consecutive natural number= n(n+1)^2/4
- Average of n consecutive even number= n+1
- Average of square of n consecutive even number= 2(n+1)(2n+1)/3
- Average of n consecutive odd number=n
- If each one of the given number is multiplied by constant K,their Average is multiplied by K.
- Average speed= Total distance/ distance
- If a car cover some journey from A to B at u km/hr, and the return trip at v km/hr. then the average speed during the whole journey is,
(2uv/u+v) km/hr.
11. Average of three different speeds u, v, w to travel equal distance
= 3uvw/ uv+vw+uw
12. Geometric mean of number X1, X2, X3…………Xn= n(X1*X2*X3….Xn)^1/2
Example:
Deepak took five English test during the semester and the average of his test was 86. If the average after the first three test was 84, what was the average off his fourth and fifth tests?
Solution.
We are given the Average of Deepak five test which is 86.
now, from the formula of average,
Sum of all values/Number of values= Average
Applying the same formula to our problem, we get
Sum of all values/5= 86
Sum of all test scores= 86*5=430
Also, we are given that the average of the first 3 test is 84.
Sum of first 3 test score/3=84
Sum of first 3 test score=84*3= 252
Now, we are asked to find the average of the last two test. for this, we first find the sum of the scores of the last two tests and divided the same by 2 to get the desired result.
Sum of the last two scores
=Sum of all the test scores- Sum of first 3 test scores
=430-252
=178
Average of last two tests
= Sum of the last two scores/2
= 178/2
=89