Important Formula: Averages

# Important Formula: Averages | Quantitative Aptitude for SSC CGL PDF Download

## Basic Averages Formulas

Mathematically, it is defined as the ratio of summation of all the numbers to the number of units present in the list.

OR

### Average Speed and Velocity Formula

Average speed is the total distance covered by a body within a specific time interval. The calculation of average speed involves the use of the formula provided below.

Case 1: When one travels at speed ‘a’ for half the time and speed ‘b’ for other half of the time. Then, average speed is the arithmetic mean of the two speeds.
Average Speed=

Case 2: When one travels at speed ‘a’ for half of the distance and speed ‘b’ for other half of the distance.Then, average speed is the harmonic mean of the two speeds.
Average Speed=

Case 3: When one travels at speed a for one-third of the distance, at speed b for another one-third of the distance and speed c for rest of the one-third of the distance
or:
Average Speed =

Average Velocity: It can be defined as total displacement divided by total time. We calculate Average Velocity using the below formula
Average Velocity =

Formula of Averages Related to Numbers:

• Average  of ‘n’ consecutive Natural Numbers =
• Average of the square of consecutive n natural numbers =
• Average of cubes of consecutive n natural numbers =
• Average of n consecutive even numbers = (n+1)
• Average of consecutive even numbers till n =
• Sum of 1st n even consecutive natural numbers is =  n(n + 1)
• Sum of 1st n odd consecutive natural numbers is = n2

Q1: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Sol:
Average of 10 numbers = 23
Sum/Total numbers = 23
Sum/10 = 23
Sum of the 10 numbers = 230
If each number is increased by 4, the total increase = 4 x 10 = 40
New sum = 230 + 40 = 270
Therefore, the new average = 270/10 = 27

Q2: The mean of 25 numbers is 36. If the mean of the first numbers is 32 and that of the last 13 numbers is 39, find the 13th number.
Sol:

Mean of the first 13 numbers = 32
Sum of the first 13 numbers = (32 × 13) = 416
Mean of the last 13 numbers = 39
Sum of the last 13 numbers = (39 × 13) = 507
Mean of 25 numbers = 36
Sum of all the 25 numbers = (36 × 25) = 900
Therefore, the 13th observation = (416 + 507 – 900) = 23
Hence, the 13th observation is 23

Q3: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Sol:

Let the average after 7th inning = x
Then average after 16th inning = x – 3
16(x-3)+87 = 17x
x = 87 – 48 = 39

Q4: The average weight of a group of seven boys is 56 kg. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy.
Sol:

Average weight of 7 boys = 56 kg.
Total weight of 7 boys = (56 × 7) kg = 392 kg.
Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg
= 338 kg.
Weight of the 7th boy = (total weight of 7 boys) – (total weight of 6 boys)
= (392 – 338) kg
= 54 kg.
Therefore, the weight of the seventh boy is 54 kg.

Q5: The average of 7 consecutive numbers is 20. What is the largest of these numbers?
Sol:

Let the 7 consecutive numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
As per the given condition;
[x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)] / 7 = 20
⇒ 7x + 21 = 140
⇒ 7x = 119
⇒ x =17
The largest number = x + 6 = 23.

The document Important Formula: Averages | Quantitative Aptitude for SSC CGL is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
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## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

335 videos|201 docs|244 tests

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