Question

the arithmetic mean of the set of observation 1,2,3,4.....n is

Answer 1

Hey there!
1 , 2 , 3 , ......, n forms an Arithmetic progression.

First term = 1
Last term = n
Common difference = 2 - 1 = 1 .
Number of terms = n

We know that, Sum of all terms of an A. P with numbers of terms n & first and last terms are a, l respectively = n/2 [ a + l ]

Now, For the Given A. P
Sum of n terms = n/2 [ 1 + n ] = n ( n + 1 )/2 .

We know that,
Arithmetic mean is the ratio of Sum of observations to Number of observations .

Arithmetic mean = Sum of observations / Number of observations.

Arithmetic mean = (n ( n + 1 ) / 2 ) / n =n(n+1)/(2n) = n+1/2 .

$\therefore$ The Arithmetic mean of the series 1 , 2 , 3 , ... , n = n + 1 /2 .

Hope helped!

Answer 2

Answer:

Step-by-step explanation



The arithmetic mean of the set of observation 1,2,3,4.....n

Solution..

1 , 2 , 3 , ......, n forms an Arithmetic progression.

First term = 1

Last term = n

Common difference = 2 - 1 = 1 .

Number of terms = n

We know that, Sum of all terms of an A. P with numbers of terms n & first and last terms are a, l respectively = n/2 [ a + l ]

Now, For the Given A. P

Sum of n terms = n/2 [ 1 + n ] = n ( n + 1 )/2 .

We know that,

Arithmetic mean is the ratio of Sum of observations to Number of observations .

Arithmetic mean = Sum of observations / Number of observations.

Arithmetic mean = (n ( n + 1 ) / 2 ) / n =n(n+1)/(2n) = n+1/2 .

\therefore The Arithmetic mean of the series 1 , 2 , 3 , ... , n = n + 1 /2 .

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