Arithmetic Mean Questions

Arithmetic Mean questions and answers will assist students in quickly grasping the topic. Almost every board exam incorporates a variety of arithmetic mean questions. Students can use these questions to summarise the topics briefly and practise answering them to improve their knowledge. Learn the complete explanations for each question to verify your answers. To understand more about the arithmetic mean, click here.

Arithmetic Mean Questions with Solutions

1. Find the arithmetic mean of the first 10 prime numbers.

Solution:

As we know, the first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Here,

The sum of observations = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 +29 = 129

Number of observations = 10

The arithmetic mean = Sum of observations / Number of observations.

Hence, arithmetic mean = 129/10

Arithmetic mean = 12.9.

2. Determine the “k” value if the arithmetic mean of 9, 8, 10, k, 12 is 15.

Solution:

Given that, the mean of 5 numbers is 15.

i.e. (9 + 8 + 10 + k + 12)/5 = 15

Hence, we get

(39 + k)/5 = 15

Now, simplify the above equation, and we get

⇒ 39 + k = 15 × 5

⇒ 39 + k = 75

Now, subtract 39 on both sides, we get

⇒ 39 – 39 + k = 75 – 39

⇒ k = 36

Hence, the value of k is 36.

3. The mean of 14 numbers is 6. What will be the new mean if 3 is added to every number?

Solution:

Assume that the given numbers be a₁, a₂, a₃, ….. a₁₄.

Therefore, the mean of these numbers = (a₁ + a₂ + a₃+ ….. a₁₄)/14

Therefore, (a₁ + a₂ + a₃+ ….. a₁₄)/14 = 6

The above equation can be written as:

⇒ a₁ + a₂ + a₃+ ….. a₁₄ = 84 …(1)

To find: New mean if 3 is added to every number.

Therefore, the new numbers are (a₁ + 3), (a₂ + 3), (a₃ + 3), …. ,(a₁₄ + 3)

Mean of the new numbers = (a₁ + 3) + (a₂ + 3)+(a₃ + 3)+ …. +(a₁₄ + 3)/14

The above form can be written as:

Mean of new numbers = [(a₁ + a₂ + a₃+ ….. a₁₄) + 42]/14

Now, use the equation (1), and we get

Mean of new numbers = (84 + 42)/14

Simplifying the values, we get

= 126/14

= 9

Therefore, the new mean obtained is 9.

4. The arithmetic mean of 40 numbers was found to be 38. It was then discovered that the number 56 had been misinterpreted as 36. Determine the correct mean of the numbers given.

Solution:

The calculated arithmetic mean of 40 numbers is 38.

Hence, the sum of these numbers = (38 × 40) = 1520.

Thus, the actual sum of these numbers = [1520 – (Incorrect value) + (correct value)]

Correct Mean = 1520 – 36 + 56

Correct Mean = 1540.

Hence, the correct mean of the given numbers = 1540/40 = 38.5.

5. The arithmetic mean of the first five numbers is 28. The mean is reduced by two when one of the numbers is removed. Find the number that isn’t included.

Solution:

Given that, the arithmetic mean of 5 numbers = 28.

Thus, the sum of these 5 numbers = (28 x 5) = 140.

Also, given that the mean is reduced by two when one of the numbers is removed.

i.e. The mean of the remaining 4 numbers = (28 – 2) =26.

Therefore, the sum of these remaining 4 numbers = (26 × 4) = 104.

Thus, the number that is not included = (sum of the given 5 numbers) – (sum of the remaining 4 numbers)

= 140 – 104

= 36

Hence, the excluded number is 36.

6. P and Q have an average monthly salary of Rs. 5050. Q and R have an average monthly income of Rs. 6250, while P and R have an average monthly income of Rs. 5200. Find the monthly salary of P.

Solution:

Assume that A, B and C represent the monthly income of P, Q, and R, respectively. So, we have

A + B = (5050×2) = 10100….(1)

B + C = (6250×2) = 12500…..(2)

A + C = (5200×2) = 10400….(3)

Now, add the equations 1, 2 and 3:

2(A+B+C) = 33000

The above equation can also be written as:

A + B + C = 33000/2 = 16500…(4)

Now, subtract (2) from (4), we get A = 4000.

Therefore, P’s monthly income is Rs.4000.

7. For successive three years, a car owner purchases petrol at Rs.7.50, Rs. 8, and Rs. 8.50 a litre. If he spends Rs. 4000 per year on petrol, what is the average cost per litre?

Solution:

Total amount of petrol consumed over three years = [(4000/7.50)+(4000/8)+4000/8.50)] litres

= 4000[(2/15) +(⅛) + (2/17)] litres

Total = 76700/51 litres

Amount spent in total = Rs. (3 × 4000) = Rs. 12000.

Thus, the average cost = Rs. (12000 × 51) /76700

Hence, the average cost per litre is Rs. 7.98.

8. A class of 16 boys has an average weight of 50.25 kg, while the remaining 8 boys have an average weight of 45.15 kg. Calculate the average weight of all boys in the class.

Solution:

16 boys in a class have an average weight of 50.25kg

8 boys in a class have an average weight of 45.15kg

Thus, the required average = [(50.25×16) + (45.15×8)] / (16 + 8)

= ( 804+361.20) / 24

∴ Required average = 1165.20 / 24

= 48.55 kg

Therefore, the average weight of all boys in the class is 48.55 kg.

Also, read: Average.

9. The marks of a student were entered incorrectly as 83 instead of 63. As a result, the class’s average marks increased by half (1/2). Find the number of students in the class.

Solution:

Let’s say the class has x students.

As a result, the overall increase in mark = (x × 1/2) = x/2.

x/2 = 83 – 63

x/2 = 20

x = 40.

Hence, the number of students in the class is 40.

10. 36 is the arithmetic mean of 25 observations. Find the 13th observation if the mean of the first observation is 32 and the final 13 observations are 39.

Solution:

The first 13 observations have a mean of 32.

The sum of the first 13 observations is 416, i.e. 32 × 13 = 416.

The average of the last 13 observations is 39.

The sum of the last 13 observations is 507, i.e. 39 × 13 = 507

The average of the 25 observations is 36.

The total of all 25 observations is (36 × 25) = 900.

As a result, the thirteenth observation equals (416 + 507 – 900) = 23.

Therefore, the thirteenth observation is 23.

Explore More Articles

• Average Questions
• Median Questions
• Data Handling Questions
• Sequence Questions
• Series Questions
• Factorisation Questions

Practice Questions

1. Find the arithmetic mean of the first 5 multiples of 5.
2. The arithmetic mean of eight numbers is 25. What will the new mean be if 5 is deducted from each number?
3. A, B, and C all weigh 45 kg on average. What is the weight of B if the average weight of A and B is 40 kg and the average weight of B and C is 43 kg?

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