In this Arithmetic Average Quiz 10, you will practice question relation to bank and Insurance like SBI Clerk Pre, IBPS Clerk Pre, IBPS RRB Pre, Railways, UIIC, LIC, NIACL, NICL, OICL and other competive exams
Here we are going to discuss about Average concept, Tricks and Shortcuts for all bank, SSC, Insurance and Railways Exams.
Average is most important part for all competitive exams, in each exam generally one has asked from Average chapter.
Let discuss about Average with suitable examples
Introduction:
An average or an arithmetic mean of given data is the sum of the given observations divided by number of observations.
|
Average = |
( |
Sum of observations |
) |
. |
|
Numbers of observations |
|
For example, if a batsman scores 35, 45 and 37 runs in first, second and third innings respectively, then his Average runs in 3 innings
|
= |
35 + 45 + 37 |
= 39 runs. |
|
3 |
Therefore, the two mostly used formulas in this chapter are:
|
Average = |
Total of data |
|
No. of data |
|
&
|
|
|
Total = Average × No. of data |
|
Properties of Average:
1. Average of a given data is less than the greatest observation and greater than the smallest observation of the given data.
For example, average of 3, 7, 9 and 13
|
= |
3 + 7 + 9 + 13 |
= |
32 |
= 8 |
|
4 |
4 |
Clearly, 8 is less than 13 and greater than 3.
2. If the observations of given data are equal, then the average will also be the same as observations.
For example, average of 6, 6, 6 and 6 will be 6 because
|
= |
6 + 6 + 6 + 6 |
= |
24 |
= 6 |
|
4 |
4 |
3. If 0 (zero) is one of the observation of a given data then that 0 (zero) will also be included while calculation average.
For example, average of 3, 6 and 0 is 3 because
Remember
• If the value of each item in a group is increased/decreased by the same value x, then the average of the group also increases/decreases by x. For instance, if the income of each person in a group increases by 15, the average income of the group also increases by Rs. 15.
This is valid only when the value of each item increases/decreases by the same amount.
• If the average age of group of people is x years, then their average age after n years will be (x + n) and their average age n years ago would have been (x – n) years.
This is because with each passing year, each person’s age increases by 1 and vice versa.
• If the value of each item in a group is multiplied/divided by the same value x (where x ≠ 0 in the case of division), then the average of the group also gets multiplied/divided by x.
Ex. The average weight of 4 men is increased by 3 kg when one of them who weighs 120 kg is replaced by another man. What is the weight of the new man?
Sol. If the average is increased by 3kg, then the sum of weights increases by 3 × 4 = 12 kg.
And this increase in weight is due to the extra weight included due to the inclusion of new person.
∴ Weight of new man = 120 + 12 = 132 kg
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