Question

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

Answer 1

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 .

Answer 2

Answer:

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