Average

Average: Formulas, Tricks, Examples and Online Test

Average refers to the sum of numbers divided by n. Also called the mean average.

Sums of data divided by the number of items in the data will give the mean average. The mean average is used quite regularly to determine final math marks over a term or semester. Averages are often used in sports: batting averages which means number of hits to number of times at bat. Gas mileage is determined by using averages.

Hence, average =

For Example: To find the average of 3, 5 and 7.

Solution

Step 1: Find the sum of the numbers.

3 + 5 + 7 = 15

Step 2: Calculate the total number.

There are 3 numbers.

Step 3: Finding average 15/3 = 5

Quicker Method to Solve the Questions

Sum of elements = average × no. of elements

Example 1: The average of marks obtained by 4 students in a class is 65. Find the sum of marks obtained?
Solution. Here, number of marks obtained = 4

Average = 65

∴ sum of marks obtained = 65 × 4 = 260

Number of elements =

Example 2: If the sum of elements and average are respectively 65 and 13, then find the number of elements.

Solution. Number of elements = =

Average of a group consisting of two different groups whose averages are known:
Let a group with average a contain m quantities and another group of n quantities whose average is b, then the average of group c containing at a + b quantities

Example 3: There are 30 students in a class. The average age of the first 10 students is 12.5 years. The average age of the next 20 students is 13.1 years. Find the average age of the whole class.

Solution.Total age of 10 students = 12.5 × 10 = 125 years

Total age of 20 students = 13.1 × 20 = 262 years

∴ Average age of 30 students = = = 12.9 years

If in a group one or more new quantities are added or excluded, then new quantity or sum.
= [change in no. of quantities × original average] ±
[change in average × final no. of quantities]
Take + ve sign if quantities added and take –ve sign if quantities removed

Example 4: The average weight of 24 students in a class is 35 kg. if the weight of the teacher is included, the average weight rises by 400 gms. find the weight of the teacher.

Solution.Total weight of 24 students = (24 × 35) kg = 840 kg

Total weight of 24 students and the teacher = (25 × 35.4) kg = 885 kg

∴ Weight of teacher = (885 – 840) kg = 45 kg

Average Exercise

What is the average of the following set of numbers?965, 362, 189, 248, 461, 825, 524, 234
- 476
- 504
- 461
- 524
What is the average of the following set of numbers?341, 292, 254, 375, 505, 639
- 401
- 399
- 405
- 397
What is the average of the following set of numbers?118, 186, 138, 204, 175, 229
- 148
- 152
- 156
- 175
What is the average of the following set of numbers?178, 863, 441, 626, 205, 349, 462, 820
- 505
- 441
- 349
- 493
What is the average of the following set of numbers?361, 188, 547, 296, 656, 132, 263
- 278
- 449
- 349
- 296
If 25a + 25b = 115, then what is the average of a and b?
- 4.6
- 2.3
- 4.5
- 3.4
If the value of 16a + 16b = 672, what is the average of a and b?
- 44
- 21
- 24
- 42
If 37a + 37b = 5661, what is the average of a and b?
- 74.5
- 151
- 76.5
- 153
If the mean of the numbers 27 + x, 31 + x, 89 + x, 107 + x, 156 + x is 82, then the mean of 130 + x, 126 + x, 68 + x, 50 + x, 1 + x is:
- 75
- 157
- 82
- 80
The average of two numbers is XY. If one number is X, then the other number is
- Y
- Y/2
- 2XY – X
- X (Y – 1)
The average of 5 consecutive even numbers A, B,C,D and E is 52. What is the product of B and E?
- 2916
- 2988
- 3000
- 2800
The average of 5 consecutive odd numbers A, B, C, D and E is 41. What is the product of A and E?
- 1977
- 1517
- 1665
- 1591
The average of 5 consecutive even number A, B, C, D and E is 34. What is the product of B and D?
- 1088
- 1224
- 1368
- 1152
The average of four consecutive odd numbers is 12.Which is the lowest odd number?
- 9
- 3
- 5
- Cannot be determined
The average of five consecutive odd numbers is 61. What is the difference between the highest and the lowest number?
- 8
- 2
- 5
- Cannot be determined
The average of three consecutive odd numbers is 14 more than one-third of the first of these numbers, what is the last of these numbers?
- 17
- 19
- 15
- Data inadequate
The average of four consecutive even numbers is one-fourth of the sum of these numbers. What is the difference between the first and the last number?
- 4
- 6
- 2
- Cannot be determined
The average of five numbers is 281. The average of the first two numbers is 280 and the average of the last two numbers is 178.5. What is the third number?
- 488
- 336
- 228
- 464
Out of the three given numbers, the first number is twice the second and thrice the third. If the average of the three numbers is 121, what is the difference between the first and the third number?
- 132
- 99
- 77
- 144
The average of the first and the second of three numbers is 15 more than the average of the second and the third of these numbers. What is the difference between the first and the third of these three numbers?
- 15
- 45
- 60
- 30
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
- 0
- 1
- 10
- 19
The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
- 4.5
- 4.6
- 4.7
- 4.8
The average of 10 numbers is 40.2 Later it is found that two numbers have been wrongly copied. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
- 40.2
- 40.4
- 40.6

courtesy:https://www.edudose.com/maths/average-exercise/

Q.1. The average marks of 13 papers is 40. The average marks of the first 7 papers are 42 and that of the last seven papers is 35. Find the marks obtained in the 7th paper.Q.2. Mukul has earned as an average of 4,200 dollars for the first eleven months of the year. If he justifies his staying in the US on the basis of his ability to earn at least 5000 dollars per month for the entire year, then how much should he earn (in dollars) in the last month to achieve his required average for the whole year?Q.3. The average of x, y and z is 45. x is as much more than the average as y is less than the average. Find the value of z.Q.4. The average for some number of terms (say ‘n’ ) is zero. How many maximum numbers of terms can be negative?Q.5. The average salary of 30 officers in a firm is Rs.120 and the average salary of laborers is Rs. 40. Find the total number of laborers if the average salary of the firm is Rs. 50.Q.6. In a class, the average marks of 40 students was calculated to be 52.15. It was later discovered that the marks of a student were taken to be 49, instead of 85. Find the real average of the class.Q.7. For 9 innings, Aman has a certain run rate. In the tenth inning, he scores 100 runs, thereby increasing his run rate by 8 runs. What is his new run rate?Q8. The average of 5 consecutive numbers is n. What will be the average if the next two numbers are included?Q9. In 40 overs game, in first 20 overs of a game of cricket, the run rate was only 5. What should be the run rate for the remaining overs so that the total score reaches 300?Q10. The average weight of 39 men travelling to Ladakh is 30. If an obese man with weight 130 kg join them. What will be the average weight of the people travelling to Ladakh?

Courtesy:https://www.hitbullseye.com/Average-Practice-Questions.php

Tutorial Video: