Question

14. The average of 50 numbers is 38.
two numbers, namely 45 and 55
are discared, the average of
remaining numbers is
(a) 36.5 (b) 37 (C) 37.5 (d) 37.​

Answer 1

$\Huge{\underline{\boxed{\textbf{\green{Answer\::}}}}}$

$\red{\textbf{The\:average\:of\:remaining\:number\:is\::-}}$

$\red{\textbf{(C)\:37.5}}$

• Step by step explaination :-

• $\large{\underline{\underline{Given\::}}}$

●The Average of 50 number = 38.

●Two number 45 and 55 are discarded.

• $\large{\underline{\underline{To\:find\::}}}$

Solution :-

Average of this question is 38 and total is 50.

By applying the formula :-

$\textbf{Average}$ = $\frac{Sum\:of\:observation}{Total\:number\:of\:observations}$

● Block in available data,

$\rightarrow{38\:={\frac{Sum\:of\:observations}{50}}}}$

$\rightarrow{38×50\:=\:Sum\:of\:observations}$

$\rightarrow{1900\:=\:Sum\:of\:observations.}$

So,

The two observation is discarded with 45 and 55.

The sum is equals to 100.

So, When we discard we will get the subtract sum of two numbers. which are discarded from sun of observation 1990.

So sum of observation = 1900 - 100.

The total number of obswrvation is = 48.

By let the average be x.

So apply the formula for average.

$\rightarrow$ x = $\frac{1900-100}{48}$

$\rightarrow$ x = $\frac{1800}{48}$

$\rightarrow$ x = $\textbf{37.5}$

So, Average of reamining is $\red{\textbf{37.5}}$

Answer 2

$\bold{\huge{\tt{\underline{\underline{AnsWer:}}}}}$

The average of remaining numbers is 37.5.Option→ (C)

$\bold{\huge{\tt{\underline{\underline{StEp\:by\:stEp\:explanation:}}}}}$

GIVEN :

• Average of 50 numbers = 38
• Two numbers, 45 and 55 are discarded.

TO FIND :

• Average of the remaining numbers.

SOLUTION :

In the question, average is 38 of total 50 observations.

As per the formula of average, the sum of observation is absent.

Applying the formula,

$\bold{\boxed{\large{\tt{\red{Average\:=\:{\dfrac{Sum\:of\:observation}{Total\:number\:of\:observations}}}}}}}$

Block in the available data,

↬$\tt{38\:=\:{\dfrac{Sum\:of\:observations}{50}}}$

↬$\tt{38\:\times\:50\:=\:Sum\:of\:observations}$

↬$\tt{1900=\:Sum\:of\:observations}$

Now, two observations are discarded, 45 and 55.

Sum of these two observation is 100.

After discarding :

We will subtract the sum of the two numbers which are discarded from the sum of observation i.e 1900

Sum of observation = 1900 -100 Total Number of observation = 48

Let the average be x.

Applying the formula for average,

↬$\tt{x\:=\:{\dfrac{1900-100}{48}}}$

↬$\tt{x\:=\:{\dfrac{1800}{48}}}$

↬$\tt{x\:=\:37.5}$

$\tt{\therefore{{Average\:of\:remaining\:numbers\:=\:37.5}}}$