Question

The mean of the distribution in which observations are 1, 2, 3, ---n is

Answer 1

Answer:

I can't understand it an you please repeat it

Answer 2

The mean of the distribution in which observations are 1, 2, 3, ---n is $\dfrac{n+1}{2}$.

Explanation:

We know that the sum of first n term is given by : $S_n=\dfrac{n(n+1)}{2}$

Or we can find by using Arithmetic progression :

Sum of first n terms $S_n=\dfrac{n}{2}(a+l)$

, where n =1 ,2 , 3,4 ,...

a= first term

d= common difference.

l= last term

For 1, 2, 3, ---n , a= 1 , d= 1 , l= n

then, $S_n=\dfrac{n}{2}(1+n)$

Mean = $\dfrac{Sum\ of \ observations}{Number\ of \ observations}$

⇒ Mean =$\dfrac{\dfrac{n(n+1)}{2}}{n}=\dfrac{n+1}{2}$

Hence, the mean of the distribution in which observations are 1, 2, 3, ---n is $\dfrac{n+1}{2}$.

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