Question

if mean of five observation =n, n+1,n+4,n+6, n+8 is 11 then find the value of n​

Answer 1

GIVEN :–

• Mean of five observations n, n+1,n+4,n+6, n+8 is 11.

TO FIND :–

• Value of 'n' = ?

SOLUTION :–

• We know that Mean of n terms –

$\\ \bf \implies Mean = \dfrac{x_1 +x_2 + . . . . . +x_n}{n}$

• Now –

$\\ \bf \implies \dfrac{n + n+1 + n+4 + n+6 + n+8}{5} = 11$

$\\ \bf \implies \dfrac{5n+19}{5} = 11$

$\\ \bf \implies5n+19 =55$

$\\ \bf \implies5n=55 - 19$

$\\ \bf \implies5n=36$

$\\ \large \implies{ \boxed{ \bf n= \dfrac{36}{5}}}$

Answer 2

Answer:

Given :-

• The mean of five observation is n, n + 1, n + 4, n + 6, n + 8 is 11.

To Find :-

• What is the value of n.

Solution :-

Given :

• No of observations = 5
• Mean = 11

According to the question,

$\\ \sf \implies\dfrac{n + (n + 1) + (n + 4) + (n + 6) + (n + 8)}{5} =\: 11$

$\\ \sf \implies\dfrac{n + n + 1 + n + 4 + n + 6 + n + 8}{5} =\: 11$

$\\ \sf \implies\dfrac{n + n + n + n + n + 1 + 4 + 6 + 8}{5} =\: 11$

$\sf \implies\dfrac{5n + 19}{5} =\: 11$

By doing cross multiplication we get,

$\\ \sf \implies 5n + 19 =\: 5 \times 11$

$\\ \sf \implies 5n + 19 =\: 55$

$\\ \sf \implies 5n = 55 - 19$

$\\ \sf \implies 5n =\: 36$

$\\ \sf \implies\bold{\red{n =\: \dfrac{36}{5}}}$

$\therefore$ The value of n is ${\purple{\boxed{\large{\bold{\dfrac{36}{5}}}}}}$.