The average of 10 observation is 3.5. if two observation namely 3.5 an

1.	The average of 10 observation is 3.5. if two observation namely 3.5 and 2.5 are deleted find the new average
Answer» Question :- The average of 10 observations is 3.5 . If two observations namely 3.5 and 2.5 are SUBTRACTED . Find the new average ? Answer :- Given :- The average of 10 observations is 3.5 . 2 of the observations namely 3.5, 2.5 are subtracted Required to find :- Find the new average of the remaining observations Formulae used :- $\large{\leadsto{\boxed{\rm{Mean = \dfrac{Sum \: of \; the \; observations}{Number \; of \; observations }}}}}{\bigstar}$ $\large{\leadsto{\boxed{\rm{Sum \; of \; the \; observations = Mean \times Number \; of \; observations }}}}}{\bigstar}$ Solution :- Given that, The average of 10 observations is 3.5 . If 2 of the observations namely 3.5 , 2.5 are subtracted or removed . He asked us to find the new average . So, Consider the first statement . The average of 10 observations is 3.5 No. of observations = 10 Hence, Using the formula; $\large{\leadsto{\boxed{\rm{Sum \; of \; the \; observations = Mean \times Number \; of \; observations }}}}}{\bigstar}$ So, ➾ Sum of the observations = 3.5 x 10 ➾ Sum of the observations = 35 It is also given that, If 3.5 , 2.5 are removed or subtracted from the observations So, 3.5 + 2.5 = 6.0 Here, Divide this from the WHOLE sum . So, ➾ New sum of the observations = 35 - 6 ➾ New sum of the observations = 29 Hence, New average = ? By using the formula $\large{\leadsto{\boxed{\rm{Mean = \dfrac{Sum \: of \; the \; observations}{Number \; of \; observations }}}}}{\bigstar}$ So, $\longrightarrow{\tt{ New \; average = \dfrac{ New \; sum \; of \; the \; observations }{Number \; of \; observations }}}$ Number of observations = 8 $\longrightarrow{\tt{ New \; average = \dfrac{29 }{8}}}$ $\longrightarrow{\tt{ New \; average = 3.625 }}$ $\large{\leadsto{\boxed{\rm{ New \; average = 3.625 }}}}$ Note :- A small tip to solve these solutions is whenever mean is given you need to find the sum and whenever sum is given find the mean .

The average of 10 observation is 3.5. if two observation namely 3.5 and 2.5 are deleted find the new average

Answer»

Question :-

The average of 10 observations is 3.5 . If two observations namely 3.5 and 2.5 are SUBTRACTED . Find the new average ?

Answer :-

Given :-

The average of 10 observations is 3.5 .

2 of the observations namely 3.5, 2.5 are subtracted

Required to find :-

Find the new average of the remaining observations

Formulae used :-

$\large{\leadsto{\boxed{\rm{Mean = \dfrac{Sum \: of \; the \; observations}{Number \; of \; observations }}}}}{\bigstar}$

$\large{\leadsto{\boxed{\rm{Sum \; of \; the \; observations = Mean \times Number \; of \; observations }}}}}{\bigstar}$

Solution :-

Given that,

The average of 10 observations is 3.5 .

If 2 of the observations namely 3.5 , 2.5 are subtracted or removed .

He asked us to find the new average .

So,

Consider the first statement .

The average of 10 observations is 3.5

No. of observations = 10

Hence,

Using the formula;

$\large{\leadsto{\boxed{\rm{Sum \; of \; the \; observations = Mean \times Number \; of \; observations }}}}}{\bigstar}$

So,

➾ Sum of the observations = 3.5 x 10

➾ Sum of the observations = 35

It is also given that,

If 3.5 , 2.5 are removed or subtracted from the observations

So,

3.5 + 2.5 = 6.0

Here,

Divide this from the WHOLE sum .

So,

➾ New sum of the observations = 35 - 6

➾ New sum of the observations = 29

Hence,

New average = ?

By using the formula

$\large{\leadsto{\boxed{\rm{Mean = \dfrac{Sum \: of \; the \; observations}{Number \; of \; observations }}}}}{\bigstar}$

So,

$\longrightarrow{\tt{ New \; average = \dfrac{ New \; sum \; of \; the \; observations }{Number \; of \; observations }}}$

Number of observations = 8

$\longrightarrow{\tt{ New \; average = \dfrac{29 }{8}}}$

$\longrightarrow{\tt{ New \; average = 3.625 }}$

$\large{\leadsto{\boxed{\rm{ New \; average = 3.625 }}}}$

Note :-

A small tip to solve these solutions is whenever mean is given you need to find the sum and whenever sum is given find the mean .