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
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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]