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Re: If the average(arithmetic mean) of 18 consecutive [#permalink]
amorphous wrote:
There are altogether \(18\) numbers.
Let us assume the first number is \(x\) this leaves us with 17 numbers.
Since the numbers are consecutively odd such as 3,5,7 or 11,13,15.
Notice that for odd numbers there is a gap of 2 between successive numbers hence each number after the first will be 2 more than the previous number.
Hence the numbers will be such as x,x+2,x+2+2,x+2+2+2....
therefore if the first number is x the last number or the 18th number will be \(17*2 + x\)
since each number in the sequence are equally spaced the mean will be the avg of the first and last number.
which is \(\frac{x+x+38}{2} = \frac{2(x+17)}{2} = [m]x+17\)[/m]
From question \(x+17 = 534\)
therefore, \(x = 517\)


Is it (x+x+38)/2 or (x+x+34)/2 ?
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Re: If the average(arithmetic mean) of 18 consecutive [#permalink]
AE wrote:
amorphous wrote:
There are altogether \(18\) numbers.
Let us assume the first number is \(x\) this leaves us with 17 numbers.
Since the numbers are consecutively odd such as 3,5,7 or 11,13,15.
Notice that for odd numbers there is a gap of 2 between successive numbers hence each number after the first will be 2 more than the previous number.
Hence the numbers will be such as x,x+2,x+2+2,x+2+2+2....
therefore if the first number is x the last number or the 18th number will be \(17*2 + x\)
since each number in the sequence are equally spaced the mean will be the avg of the first and last number.
which is \(\frac{x+x+38}{2} = \frac{2(x+17)}{2} = [m]x+17\)[/m]
From question \(x+17 = 534\)
therefore, \(x = 517\)


Is it (x+x+38)/2 or (x+x+34)/2 ?


Thanks for checking. It is (x+x+34)/2
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Re: If the average(arithmetic mean) of 18 consecutive [#permalink]
1
n be the first term
Last term => \(n+17*2=> n+34\)

Now as the series will be in Arithmetic progression
Mean = Average of the first and the last term
Hence 534 =\(\frac{n+n+34}{2}=> n+17\)
Hence n+17=534=> n=517

Hence A
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Re: If the average(arithmetic mean) of 18 consecutive [#permalink]
1
Given that the average(arithmetic mean) of 18 consecutive odd integers is 534 and we need to find the least of these integers

============================================================

Theory
    ‣‣‣ In Case of consecutive number with even number of term, Mean = Mean of Middle two terms

============================================================

Let the middle two terms are 2x-1 and 2x+1

=> Mean = mean of middle two terms = \(\frac{2x-1 + 2x+1}{2}\)= \(\frac{4x}{2}\) = 2x = 534

As there are 18 terms so the middle two terms will be \(9^{th}\) and \(10^{th}\) term
=> \(9^{th}\) term = 2x-1 = 534-1 = 533

First term or the lest term will be \(9^{th}\) term - 2*8 = 533 - 16 = 517

So, Answer will be A.
Hope it helps!

Watch the following video to Learn the Basics of Statistics

[you-tube]https://www.youtube.com/watch?v=Cvy_HHw4KIs[/you-tube]
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