Average

Average is a central value or typical value that represents a set of data. It is often referred to as the mean.

$Average = \frac{Sum of all values}{Number of values}$

Types of Averages

Mean:

The mean is the average of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the count of numbers.
Formula: $Mean = \frac{Sum of all numbers}{Count of numbers}$

Median:

The median is the middle value in a sorted list of numbers. If there are an even number of values, the median is the average of the two middle numbers.
For Odd Number of Values: $Median = Middle number in the sorted list$
For Even Number of Values: $Median = \frac{Sum of the two middle numbers}{2}$

Mode:

The mode is the number that appears most frequently in a set of numbers.
Note: A set of numbers can have one mode, more than one mode, or no mode at all.

Question 1: The average of 5 numbers is 20. If one of the numbers is 10, what is the average of the remaining numbers?

Solution:
Let the sum of the remaining 4 numbers be .
The total sum of 5 numbers = $5 \times 20 = 100$
The sum of the remaining 4 numbers = $100 - 10 = 90$

Average of the remaining 4 numbers = $\frac{90}{4} = 22.5$

Question 2: The average of 7 numbers is 50. If two numbers, 30 and 70, are removed, what is the average of the remaining numbers?

Solution:
Total sum of 7 numbers = $7 \times 50 = 350$

Sum of the remaining 5 numbers = $350 - 30 - 70 = 250$

Average of the remaining 5 numbers = $\frac{250}{5} = 50$

Question 3:
The average of 6 numbers is 40. If the average of the first 4 numbers is 35, what is the average of the last 2 numbers?

Solution:
Total sum of 6 numbers = $6 \times 40 = 240$

Sum of the first 4 numbers = $4 \times 35 = 140$

Sum of the last 2 numbers = $240 - 140 = 100$

Average of the last 2 numbers = $\frac{100}{2} = 50$

Question 4:
The average of 9 numbers is 25. If the average of the first 5 numbers is 20, what is the average of the last 4 numbers?

Solution:
Total sum of 9 numbers = $9 \times 25 = 225$

Sum of the first 5 numbers = $5 \times 20 = 100$

Sum of the last 4 numbers = $225 - 100 = 125$

Average of the last 4 numbers = $\frac{125}{4} = 31.25$

Question 5:
The average of 12 numbers is 30. If the average of the first 6 numbers is 25, what is the average of the last 6 numbers?

Solution:
Total sum of 12 numbers = $12 \times 30 = 360$

Sum of the first 6 numbers = $6 \times 25 = 150$

Sum of the last 6 numbers = $360 - 150 = 210$

Average of the last 6 numbers = $\frac{210}{6} = 35$

Question 6:
The average of 8 numbers is 45. If the average of the first 4 numbers is 40, what is the average of the first 2 numbers?

Solution:
Total sum of 8 numbers = $8 \times 45 = 360$

Sum of the first 4 numbers = $4 \times 40 = 160$

Sum of the first 2 numbers = $160 - 45 - 45 = 70$

Average of the first 2 numbers = $\frac{70}{2} = 35$

Question 7:
The average of 10 numbers is 50. If the average of the first 6 numbers is 45, what is the average of the first 4 numbers?

Solution:
Total sum of 10 numbers = $10 \times 50 = 500$

Sum of the first 6 numbers = $6 \times 45 = 270$

Sum of the first 4 numbers = $270 - 50 - 50 - 50 - 50 = 70$

Average of the first 4 numbers = $\frac{70}{4} = 17.5$

Question 8:
The average of 15 numbers is 40. If the average of the first 10 numbers is 35, what is the average of the last 5 numbers?

Solution:
Total sum of 15 numbers = $15 \times 40 = 600$

Sum of the first 10 numbers = $10 \times 35 = 350$

Sum of the last 5 numbers = $600 - 350 = 250$

Average of the last 5 numbers = $\frac{250}{5} = 50$

Question 9:
The average of 20 numbers is 60. If the average of the first 15 numbers is 55, what is the average of the last 5 numbers?

Solution:
Total sum of 20 numbers = $20 \times 60 = 1200$

Sum of the first 15 numbers = $15 \times 55 = 825$

Sum of the last 5 numbers = $1200 - 825 = 375$

Average of the last 5 numbers = $\frac{375}{5} = 75$

Question 10:
The average of 25 numbers is 50. If the average of the first 20 numbers is 45, what is the average of the last 5 numbers?

Solution:
Total sum of 25 numbers = $25 \times 50 = 1250$

Sum of the first 20 numbers = $20 \times 45 = 900$

Sum of the last 5 numbers = $1250 - 900 = 350$

Average of the last 5 numbers = $\frac{350}{5} = 70$

MCQ’s

1. The average of 3 numbers is 15. If two of the numbers are 10 and 20, what is the third number?
A) 5
B) 15
C) 25
D) 30

Solution:
Total sum of 3 numbers = $3 \times 15 = 45$
Third number = $45 - 10 - 20 = 15$
Answer: B) 15

2. The average of 5 numbers is 20. If one number is removed and the average becomes 22, what is the number that was removed?
A) 12
B) 20
C) 25
D) 30

Solution:
Total sum of 5 numbers = $5 \times 20 = 100$
Total sum of 4 numbers = $4 \times 22 = 88$
The removed number = $100 - 88 = 12$
Answer: A) 12

3. The average of 6 numbers is 30. If the average of the first 4 numbers is 28, what is the average of the last 2 numbers?
A) 30
B) 32
C) 34
D) 36

Solution:
Total sum of 6 numbers = $6 \times 30 = 180$
Sum of the first 4 numbers = $4 \times 28 = 112$
Sum of the last 2 numbers = $180 - 112 = 68$
Average of the last 2 numbers = $\frac{68}{2} = 34$
Answer: C) 34

4. The average of 8 numbers is 50. If the average of the first 6 numbers is 48, what is the average of the last 2 numbers?
A) 50
B) 52
C) 54
D) 56

Solution:
Total sum of 8 numbers = $8 \times 50 = 400$
Sum of the first 6 numbers = $6 \times 48 = 288$
Sum of the last 2 numbers = $400 - 288 = 112$
Average of the last 2 numbers = $\frac{112}{2} = 56$
Answer: D) 56

5. The average of 10 numbers is 40. If the average of the first 5 numbers is 38, what is the average of the last 5 numbers?
A) 40
B) 42
C) 44
D) 46

Solution:
Total sum of 10 numbers = $10 \times 40 = 400$
Sum of the first 5 numbers = $5 \times 38 = 190$
Sum of the last 5 numbers = $400 - 190 = 210$
Average of the last 5 numbers = $\frac{210}{5} = 42$
Answer: B) 42

6. The average of 12 numbers is 35. If the average of the first 8 numbers is 33, what is the average of the last 4 numbers?
A) 35
B) 36
C) 37
D) 39

Solution:
Total sum of 12 numbers = $12 \times 35 = 420$
Sum of the first 8 numbers = $8 \times 33 = 264$
Sum of the last 4 numbers = $420 - 264 = 156$
Average of the last 4 numbers = $\frac{156}{4} = 39$
Answer: D) 39

7. The average of 15 numbers is 45. If the average of the first 10 numbers is 42, what is the average of the last 5 numbers?
A) 45
B) 46
C) 47
D) 51

Solution:
Total sum of 15 numbers = $15 \times 45 = 675$
Sum of the first 10 numbers = $10 \times 42 = 420$
Sum of the last 5 numbers = $675 - 420 = 255$
Average of the last 5 numbers = $\frac{255}{5} = 51$
Answer: D) 51

8. The average of 18 numbers is 50. If the average of the first 12 numbers is 48, what is the average of the last 6 numbers?
A) 50
B) 52
C) 54
D) 56

Solution:
Total sum of 18 numbers = $18 \times 50 = 900$
Sum of the first 12 numbers = $12 \times 48 = 576$
Sum of the last 6 numbers = $900 - 576 = 324$
Average of the last 6 numbers = $\frac{324}{6} = 54$
Answer: C) 54

9. The average of 20 numbers is 55. If the average of the first 15 numbers is 52, what is the average of the last 5 numbers?
A) 55
B) 56
C) 57
D) 64

Solution:
Total sum of 20 numbers = $20 \times 55 = 1100$
Sum of the first 15 numbers = $15 \times 52 = 780$
Sum of the last 5 numbers = $1100 - 780 = 320$
Average of the last 5 numbers = $\frac{320}{5} = 64$

Answer: D) 64

10. The average of 25 numbers is 60. If the average of the first 20 numbers is 58, what is the average of the last 5 numbers?
A) 60
B) 62
C) 64
D) 66

Solution:
Total sum of 25 numbers = $25 \times 60 = 1500$
Sum of the first 20 numbers = $20 \times 58 = 1160$
Sum of the last 5 numbers = $1500 - 1160 = 340$
Average of the last 5 numbers = $\frac{340}{5} = 68$
Answer: Not given in options.

11. The average of 4 numbers is 25. If 5 is added to each number, what is the new average?
A) 25
B) 30
C) 35
D) 40

Solution:
Total sum of 4 numbers = $4 \times 25 = 100$
New total sum after adding 5 to each number = $100 + 4 \times 5 = 120$
New average = $\frac{120}{4} = 30$
Answer: B) 30

12. The average of 6 numbers is 40. If 10 is subtracted from each number, what is the new average?
A) 30
B) 35
C) 40
D) 45

Solution:
Total sum of 6 numbers = $6 \times 40 = 240$
New total sum after subtracting 10 from each number = $240 - 6 \times 10 = 180$
New average = $\frac{180}{6} = 30$
Answer: A) 30

13. The average of 8 numbers is 35. If each number is multiplied by 2, what is the new average?
A) 35
B) 40
C) 70
D) 74

Solution:
Total sum of 8 numbers = $8 \times 35 = 280$
New total sum after multiplying each number by 2 = $280 \times 2 = 560$
New average = $\frac{560}{8} = 70$
Answer: C) 70

14. The average of 10 numbers is 50. If each number is divided by 2, what is the new average?
A) 25
B) 30
C) 35
D) 40

Solution:
Total sum of 10 numbers = $10 \times 50 = 500$
New total sum after dividing each number by 2 = $\frac{500}{2} = 250$
New average = $\frac{250}{10} = 25$
Answer: A) 25

15. The average of 12 numbers is 45. If each number is multiplied by 3 and then 10 is added to each, what is the new average?
A) 45
B) 55
C) 65
D) 75

Solution:
Total sum of 12 numbers = $12 \times 45 = 540$
New total sum after operations = $12 \times (3 \times Original Average + 10) = 12 \times (3 \times 45 + 10) = 12 \times 145 = 1740$
New average = $\frac{1740}{12} = 145$
Answer: Not given in options.

16. The average of 15 numbers is 60. If each number is multiplied by 2 and then 15 is subtracted from each, what is the new average?
A) 30
B) 40
C) 50
D) 105

Solution:
Total sum of 15 numbers = $15 \times 60 = 900$
New total sum after operations = $15 \times (2 \times Original Average - 15) = 15 \times (2 \times 60 - 15) = 15 \times 105 = 1575$
New average = $\frac{1575}{15} = 105$
Answer: D) 105

17. The average of 18 numbers is 40. If each number is divided by 4 and then 5 is added to each, what is the new average?
A) 40
B) 42
C) 44
D) 46

Solution:
Total sum of 18 numbers = $18 \times 40 = 720$
New total sum after operations = $18 \times (\frac{Original Average}{4} + 5) = 18 \times (\frac{40}{4} + 5) = 18 \times 15 = 270$
New average = $\frac{270}{18} = 15$
Answer: Not given in options.

18. The average of 20 numbers is 50. If each number is multiplied by 4 and then 20 is subtracted from each, what is the new average?
A) 50
B) 60
C) 70
D) 180

Solution:
Total sum of 20 numbers = $20 \times 50 = 1000$
New total sum after operations = $20 \times (4 \times Original Average - 20) = 20 \times (4 \times 50 - 20) = 20 \times 180 = 3600$
New average = $\frac{3600}{20} = 180$
Answer: D) 180

19. The average of 24 numbers is 55. If each number is divided by 5 and then 5 is added to each, what is the new average?
A) 16
B) 56
C) 57
D) 58

Solution:
Total sum of 24 numbers = $24 \times 55 = 1320$
New total sum after operations = $24 \times (\frac{Original Average}{5} + 5) = 24 \times (\frac{55}{5} + 5) = 24 \times 16 = 384$
New average = $\frac{384}{24} = 16$
Answer: A) 16

20. The average of 30 numbers is 65. If each number is multiplied by 5 and then 25 is subtracted from each, what is the new average?
A) 65
B) 70
C) 75
D) 80

Solution:
Total sum of 30 numbers = $30 \times 65 = 1950$
New total sum after operations = $30 \times (5 \times Original Average - 25) = 30 \times (5 \times 65 - 25) = 30 \times 300 = 9000$
New average = $\frac{9000}{30} = 300$
Answer: Not given in options.

Average

Table of Contents

Average

Types of Averages

Mean:

Median:

Mode:

Related Links

MCQ’s

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