let the consecutive numbers be from 1 to 25
Sum = \(\frac{n}{2}*(first term + last term) =\) \(\frac{25}{2}*(1+25)\)
or Sum = 25*13
Therefore Mean of 25 terms will be = \(\frac{25*13}{25}\) = 13
so Mean as % of Sum = \(\frac{13}{(25*13)}*100\) = 4%
Option A

I assume when the question says "total" it means to say "sum". By definition, mean = sum/n, where n is the number of terms.

We have n = 25, so:

mean = sum / 25

so the mean is 1/25 of the sum, or 4% of the sum.

It's not important that the set consists of consecutive integers.
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Solution

• Let the numbers be \(n-12,n-11,…………. , n, ,………….n+11,n+12\)


o The mean of the above would be \(= n\)

o The sum of 25 numbers will be \(= 25n\)

o Thus, the percentage \(= n*\frac{100}{25n} = 4\)%

Thanks,
Saquib
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I guess this would be the best way to solve it. If we focus on the definition, we can indeed come to conclusion that the relation between Mean and Sum is -


Mean/Sum = 1/N, where N is the total number of terms.

With this inference in mind, it would hardly take any time to solve this question.



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Saquib
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given, mean = sum /25

1/25= 4/100...
hence mean = 4% of sum..

ans A

----------ASIDE----------------------
There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}
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For this question, let x = first value
So, x+1 = second value
x+2 = third value
.
.
.
x+24 = last value

This means x+12 is the median AND the mode

Since x+12 = the mean of the 25 numbers, we can conclude that (25)(x+12 ) = the SUM of the 25 numbers

The mean of twenty-five consecutive positive integers numbers is what percent of the total?
We must convert (x+12)/(25)(x+12) to a PERCENT
(x+12)/(25)(x+12) = 1/25
= 4/100
= 4%
Answer: A

RELATED VIDEO

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hi

13
_______
13 * 25

= 4%

thanks

Recall that the sum of n positive consecutive integers (let’s denote it by S) is equal to the mean of the n integers (let’s denote it by m) times the number of integers (i.e., n). In other words, S = m x n. Therefore, the sum of 25 positive consecutive integers is S = m x 25. That is,

m = S/25 = 4S/100 = (4/100)S

We see that the mean of 25 positive integers is 4% of their sum.

Answer: A
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I think the easiest way is to pick numbers.
I chose 1 - 25.

Mean is (25+1)/2 = 13
Sum = (# of terms) (Average) = (25) ((25+1)/2) = 325

13 = (x/100)(325)
x = 4

A

We need to find mean of twenty-five consecutive positive integers numbers is what percent of the total

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Theory

‣‣‣ Mean = Sum or Total Of All The Numbers) / (Total Number Of Numbers)

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We need to find, Mean/Total * 100% = (Total/25) / Total * 100% = 100/25% = 4%

So, Answer will be A
Hope it helps!

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