Question

The question is mean of 20 observation is 17.If in the observations, observation 40 is replaced by 12 find the new mean.

Answer 1

Answer:

15.6

Step-by-step explanation:

Given mean of 20 observations is 17

Therefore sum of the 20 observations is 17×20=340

Now one observation of value 40 is changed to 12 i.e. reduced by 28

New sum of observations=340-28=312

Therefore new mean is 312÷20=15.6

Answer 2

$\huge{\longrightarrow{\rm{ ANSWER }}}{\longleftarrow}$

Given :-

Mean of 20 observations = 17

If one of the observations 40 is replaced by 12

Required to find :-

• New Mean ?

Formulae used :-

$\large{\dagger{\boxed{\tt{ Sum \; of \; the \; observations = Mean \times No. of observations }}}}$

$\large{\dagger{\boxed{\tt{ Mean = \dfrac{Sum \; of \; the \; observations }{ Number \; of \; observations }}}}}$

Solution :-

Given that :-

Mean of 20 observations = 17

If one of the observations 40 is replaced by 12

We need to find the new mean .

So,

In order to find the new mean first we need to find the sum of the given observations

Using the formula ,

$\large{\dagger{\boxed{\tt{ Sum \; of \; the \; observations = Mean \times No. of observations }}}}$

Here,

Mean of the observations = 17

Number of observations = 20

Hence,

Sum of the observations = ?

This implies

= 17 x 20

= 340

Sum of the observations = 340

Now,

subtract 40 from the sum of the observations

This is because it is given that an observation 40 is removed from the sum of the observations

So,

340 - 40

= 300

Similarly,

Add 12 to New sum of the observations because 40 is replaced by 12

So,

300 + 12

= 312

Now using the formula

$\large{\dagger{\boxed{\tt{ Mean = \dfrac{Sum \; of \; the \; observations }{ Number \; of \; observations }}}}}$

This formula enables us to find the new mean .

So,

Sum of the observations = 312

No. of observations = 20

Mean = ?

$\longrightarrow{\rm{ Mean = \dfrac{ 312 }{20 }}}$

$\longrightarrow{\rm{ Mean = 15.6 }}$

Therefore,

New mean = 15.6