Average is mainly defined as the sum of observations divided by the number of observations. Keeping in view the Quantitative Aptitude section of any competitive exam, 1-2 questions are asked from this chapter. It is not a difficulty chapter if you know the tricks to solve the question in very less time.

- Average= (Sum of observations)/(Number of observations)

- If a person travels some distance at a speed of x km/hr and the same distance at a speed of y km/hr, then the average speed during the whole journey will be calculated by using the formula

2xy/(x+y)

If a person covers P km at x km/hr and Q km at y km/hr and R km at z km/hr, then the average speed in covering the whole distance is (P+Q+R)/(P/x+Q/y+R/z)

- When a person replaces another person then:
- If the average is increased, then

Age of new person= Age of person who left + (Increase in average * total number of persons) - If the average is decreased, then

Age of new person= Age of person who left - (Decrease in average * total number of persons)

- If the average is increased, then
- When a person joins the group:
- In case of an increase in average,

Age of new member= Previous average+ (Increase in average * Number of members including new member) - In case of decrease in average,

Age of new member= Previous average- (Decrease in average * Number of members including new member)

- In case of an increase in average,
- In the Arithmetic Progression there are two cases:
- When the number of terms is odd - the average will be the middle term.
- When number of terms is even - the average will be the average of two middle terms.

To understand the concept properly, let's try doing some questions.

Since, there difference between two consecutive terms, so the average will be taken as the middle term i.e. 27.

So, the average here will be (24 + 25)/2 = 49/2 = 24.5

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Age of new member= Previous average+ (Increase in average X Number of members including new member)

Therefore,

Age of new member = 36 + (1 × 25)

Age of new member = 36 + 25 = 61

Therefore,

Age of new member = 36 + (1 × 25)

Age of new member = 36 + 25 = 61

Therefore, Average=(30 (30+1))/(2*30)

= (30*31)/(2*31) = 15.5

Required Sale = 6500 * 6 = 39000

Sale required in 6

New average when teacher is excluded = 7

Therefore, total age of six students = 6 * 7 = 42

Therefore, age of teacher = 84 - 42 = 42

Then, 19× = 13 * 79 + 6 (×+4)

13× = 1051

× ≅81 ( approximately, as in the question approximate money is asked )

Therefore, total expenditure = 81 * 19= Rs 1539

Marks of last 7 students = 7 * 35 = 245

Marks of 7

His total runs in 9 innings will be 9×

New total; 9x + 100 = 10 (×+8)

× = 20

Therefore, new average = 20 + 8 = 28

Hence, net result is a drop of 45 for 5 people.

Hence, 9 kg is the overall drop.

(2*84*56)/(84+56)= 67.2 km/hr

- We have learnt ways to find the new average when there is replacement, addition or removal of a person in a group.
- The concept of average speed when distance is constant and speeds are different finds direct application in Time, Speed and Distance Concept.