Question

.
6. Find the mean of 25 numbers, it being given that the mean of 15 of them is 18 and the mean
of remaining ones is 13.
​

Answer 1

Given:

• Total number = 25
• Mean of 15 of total is 18
• Mean of remaining is 13

To find :

• Mean of total ?

Solution:

We are given that total numbers are 25 from which mean of 15 is 18 and mean of remaining ( 25 - 15 = 10) is 13

We know that :

• $\large{\boxed{\sf{Mean\:=\:\dfrac{sum\:of\: observation}{number\:of\: observation}}}}$

Condition 1st:

• Mean = 18
• Number of observation = 15

$\implies{\large{\sf{Mean\:=\:\dfrac{sum\:of\: observation}{number\:of\: observation}}}}$

$\implies{\large{\sf{18\:=\:\dfrac{sum\;of\: observation}{15}}}}$

$\implies{\large{\sf{sum\:of\: observation\:=\: 18 × 15 }}}$

$\implies{\large{\sf{Sum\:of\: observation\:=\: 270\:\:\:\:\:\:\:••••••(i)}}}$

Condition 2nd:

• Mean = 13
• Number of observation = 10

$\implies{\large{\sf{Mean\:=\:\dfrac{sum\:of\: observation}{number\:of\: observation}}}}$

$\implies{\large{\sf{13\:=\: \dfrac{sum\:of\: observation}{10}}}}$

$\implies{\large{\sf{sum\:of\: observation\:=\: 13×10}}}$

$\implies{\large{\sf{sum\:of\: observation\:=\: 130\:\:\:\:\:\:••••••(ii)}}}$

__________________

Now, we have :

• Number of observation = 25
• Sum of observation = 270 + 130

$\implies{\large{\sf{Mean\:=\:\dfrac{sum\:of\: observation}{number\:of\: observation}}}}$

$\implies{\large{\sf{Mean\:=\:\dfrac{270+130}{25}}}}$

$\implies{\large{\sf{Mean\:=\: \dfrac{400}{25}}}}$

$\implies{\large{\sf{Mean\:=\:16}}}$

Therefore,

• $\large{\boxed{\bf{\purple{Mean\:of\:25\: numbers\:is\:16}}}}$

Answer 2

Answer:

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