Class 10 Exam > Class 10 Questions > The mean of 15 numbers is 25. If each number ...
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The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is
- a)100
- b)60
- c)10
- d)40
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The mean of 15 numbers is 25. If each number is multiplied by 4, mean ...
We have So, Mean = 
So Mean =
=25
If 4 is multiplied by each observation
So Mean =
Taking common 4 from numerator=4
=4*25=100
So Mean =
=25If 4 is multiplied by each observation
So Mean =
Taking common 4 from numerator=4
=4*25=100Most Upvoted Answer
The mean of 15 numbers is 25. If each number is multiplied by 4, mean ...
To find the answer simply multiply the mean by the given no. i.e. 4 explanation let sum of all 15 no. is x let new sum = 4x mean = x / 15 = 25 new mean= 4x/15 4(x/15) 4(25) answer=100
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Community Answer
The mean of 15 numbers is 25. If each number is multiplied by 4, mean ...
Given:
- Mean of 15 numbers = 25
To find:
- Mean of the new numbers after multiplying each number by 4
Solution:
To find the mean of a set of numbers, we sum up all the numbers and divide the sum by the total count of numbers.
Step 1: Finding the sum of the original 15 numbers.
- Mean = Sum of numbers / Total count of numbers
- 25 = Sum of numbers / 15
Step 2: Finding the sum of the new numbers after multiplying each number by 4.
- Let's assume the original numbers are represented by x1, x2, x3, ..., x15.
- The new numbers after multiplying each number by 4 will be 4x1, 4x2, 4x3, ..., 4x15.
- Sum of the new numbers = 4x1 + 4x2 + 4x3 + ... + 4x15
- Since 4 is a constant factor, it can be taken out of the sum: 4(x1 + x2 + x3 + ... + x15)
- The sum of the original numbers is equal to the sum of the new numbers divided by 4.
- Sum of the original numbers = Sum of the new numbers / 4
Step 3: Finding the mean of the new numbers.
- Mean of the new numbers = Sum of the new numbers / Total count of numbers
- Mean of the new numbers = (Sum of the original numbers) / (Total count of numbers)
- Mean of the new numbers = (Sum of the new numbers / 4) / (Total count of numbers)
- Mean of the new numbers = (Sum of the new numbers) / (4 * Total count of numbers)
- Mean of the new numbers = (Sum of the new numbers) / (4 * 15)
From Step 2, we know that the sum of the new numbers is equal to the sum of the original numbers multiplied by 4.
Sum of the new numbers = (Sum of the original numbers) * 4
Sum of the new numbers = 25 * 4 = 100
Mean of the new numbers = (Sum of the new numbers) / (4 * 15)
Mean of the new numbers = 100 / (4 * 15)
Mean of the new numbers = 100 / 60
Mean of the new numbers = 5/3
Since the mean of the new numbers is 5/3, none of the given options (A, B, C, D) match the correct answer. Therefore, there seems to be an error in the question or options provided.
- Mean of 15 numbers = 25
To find:
- Mean of the new numbers after multiplying each number by 4
Solution:
To find the mean of a set of numbers, we sum up all the numbers and divide the sum by the total count of numbers.
Step 1: Finding the sum of the original 15 numbers.
- Mean = Sum of numbers / Total count of numbers
- 25 = Sum of numbers / 15
Step 2: Finding the sum of the new numbers after multiplying each number by 4.
- Let's assume the original numbers are represented by x1, x2, x3, ..., x15.
- The new numbers after multiplying each number by 4 will be 4x1, 4x2, 4x3, ..., 4x15.
- Sum of the new numbers = 4x1 + 4x2 + 4x3 + ... + 4x15
- Since 4 is a constant factor, it can be taken out of the sum: 4(x1 + x2 + x3 + ... + x15)
- The sum of the original numbers is equal to the sum of the new numbers divided by 4.
- Sum of the original numbers = Sum of the new numbers / 4
Step 3: Finding the mean of the new numbers.
- Mean of the new numbers = Sum of the new numbers / Total count of numbers
- Mean of the new numbers = (Sum of the original numbers) / (Total count of numbers)
- Mean of the new numbers = (Sum of the new numbers / 4) / (Total count of numbers)
- Mean of the new numbers = (Sum of the new numbers) / (4 * Total count of numbers)
- Mean of the new numbers = (Sum of the new numbers) / (4 * 15)
From Step 2, we know that the sum of the new numbers is equal to the sum of the original numbers multiplied by 4.
Sum of the new numbers = (Sum of the original numbers) * 4
Sum of the new numbers = 25 * 4 = 100
Mean of the new numbers = (Sum of the new numbers) / (4 * 15)
Mean of the new numbers = 100 / (4 * 15)
Mean of the new numbers = 100 / 60
Mean of the new numbers = 5/3
Since the mean of the new numbers is 5/3, none of the given options (A, B, C, D) match the correct answer. Therefore, there seems to be an error in the question or options provided.
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The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers isa)100b)60c)10d)40Correct answer is option 'A'. Can you explain this answer?
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