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The mean of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
- a)19
- b)1
- c)10
- d)More than one of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The mean of 20 numbers is zero. Of them, at the most, how many may be ...
Understanding the Problem
To solve the problem, we start with the information provided: the mean of 20 numbers is zero. This means that the sum of these 20 numbers must also be zero.
Mean Calculation
- Mean = (Sum of all numbers) / (Total numbers)
- Given that the mean is zero:
- Sum of all numbers = 0
Implications of the Sum Being Zero
- If we have numbers greater than zero, we need corresponding numbers that are less than zero (or negative) to balance the sum back to zero.
- For instance, if there are more positive numbers, the negative numbers must compensate sufficiently to maintain a zero sum.
Maximum Positive Numbers
- If we want to maximize the count of positive numbers, we can have 19 numbers greater than zero.
- However, to maintain the sum of zero, the 20th number must be negative, and its value must equal the sum of the positive numbers.
Example Scenario
- Let’s consider an example:
- If 19 numbers are 1, the sum of these would be 19.
- To keep the total sum zero, the 20th number must be -19.
- This ensures that the sum remains zero (19 + (-19) = 0).
Conclusion
- Therefore, the maximum number of numbers that can be greater than zero, while still keeping the sum of all numbers zero, is 19.
- Hence, the correct answer is option 'A' – at most 19 numbers can be greater than zero.
To solve the problem, we start with the information provided: the mean of 20 numbers is zero. This means that the sum of these 20 numbers must also be zero.
Mean Calculation
- Mean = (Sum of all numbers) / (Total numbers)
- Given that the mean is zero:
- Sum of all numbers = 0
Implications of the Sum Being Zero
- If we have numbers greater than zero, we need corresponding numbers that are less than zero (or negative) to balance the sum back to zero.
- For instance, if there are more positive numbers, the negative numbers must compensate sufficiently to maintain a zero sum.
Maximum Positive Numbers
- If we want to maximize the count of positive numbers, we can have 19 numbers greater than zero.
- However, to maintain the sum of zero, the 20th number must be negative, and its value must equal the sum of the positive numbers.
Example Scenario
- Let’s consider an example:
- If 19 numbers are 1, the sum of these would be 19.
- To keep the total sum zero, the 20th number must be -19.
- This ensures that the sum remains zero (19 + (-19) = 0).
Conclusion
- Therefore, the maximum number of numbers that can be greater than zero, while still keeping the sum of all numbers zero, is 19.
- Hence, the correct answer is option 'A' – at most 19 numbers can be greater than zero.
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Community Answer
The mean of 20 numbers is zero. Of them, at the most, how many may be ...
Given: The mean of 20 numbers is zero
Concept used: We simply write the formula and check the terms greater than 0.
Solution:
Means of 20 numbers would be
= (n1 + n2 +...+ n20)/20 = 0
Now we take at most case -
let us assume n1, n2, ...n19 are greater then 0
then n20 = -(n1 + n2 +...+ n19)
Hence, in at most case there are 19 elements which is greater than 0.
So, there are 19 numbers which are greater than zero
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