: Get the average concept right #IndiaNEWS #Education Today Hyderabad: These series of articles on the arithmetic will aid you in your preparation for government recruitment tests. In most competitive

Get the average concept right #IndiaNEWS #Education Today
Hyderabad: These series of articles on the arithmetic will aid you in your preparation for government recruitment tests. In most competitive exams like SI, Constable, Groups, etc. , there are direct questions from the Average topic. Sometimes, questions are application-based, which require a great amount of logical thinking.
The government job aspirants need to develop a logical approach to answer the problems in this area. It is better to avoid formula-based approach to save time in exam. Let us go into the topic and try to observe the logic in basic problems.
Average: We use the word average or arithmetic mean in our daily observation. Example: Average marks, average rainfall, batting and bowling averages.
‘Average’ is most likely to be the value around which a group of values show a tendency to concentrate. Thus, we can say that average represents on entire group by single value.
Important points:
1. Highest observation contributes lower observation to balance it.
Example: If A, B are two persons having Rs 2 and Rs 4 respectively
If B gives Rs 1 to A, then A has Rs 3
Now B has Rs 3
This is called average.
2. The average always lies between the lowest and highest number of the set.
Average of a given term always lies in the range at given data.
i. e. , lowest quantity
The average of 2,4 is 3
2 < 3 < 4
Example 2: The average of 6, 6, 6 is 6.
6≤6≤6
Note: If quantities of the data are equal, then the average will also be the same as quantities
3. If ‘A’ be the average of x 1, x 2…. . x m, y1 , y2…. yn where x 1, x 2…. xm be below A and y1 and y2…. yn be above A, then
(A- x1) (A- x 2) …… (A- x n) = (y1-A) ( y2-A) (yn-A)
i. e. , the surplus above of the average is always equal the net deficit below average
Example: The average of 100, 200, 300, 400, 500 is 300.
Sum of the values of below 300 is 100 200 = 300
The average deficit = 300 (300/2)
= 300 -150 = 150
Sum of the values of above 300 is 400 500 = 900
The average surplus = (900/2) 300
= 450 300 = 150
Hence the surplus above the average = below the average.
4. If the value of each item in a group is increased / decreased by the same value, say x, then the average of the group also increases/decreases by x.
Example 1: The average of 5 numbers is 20. If 2 is added to each number, then the new average is 20 2 = 22.
Example 2: The average of 7 numbers is 37. If 3 is subtracted from each number then the new average is 37-3 = 34. This concept is useful while dealing with the problems on age.
5. If the value of each item in a group is multiplied by the same value x, then the average of the group is also multiplied by x.