Question

answer this question with explanation​

Answer 1

Answer ;

Given :

Mean marks obtained by 300 students in a subject are 60 .

Mean marks of top 100 students is 80 .

Mean marks of last 100 students is 50 .

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Required to find :

1. Mean marks of remaining students .

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Formulas used :

$\longrightarrow{\boxed{\tt{Mean \; = \; \dfrac{Sum\;of\;the\;observations}{No. \; of \; observations}}}}$

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

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Explanation :

In the question it is given that ;

1. Mean marks of all 300 students in a subject is 60 .

2. However, Mean marks of Top 100 students is 80 .

3. Similarly, Mean marks of last 100 students is 50.

He asked us to find the mean of remaining students .

Consider the above 3 statement.

Now using this 3 statements we can solve this question .

Statement - 1

Mean marks of all 300 students is 60 .

Here, in this statement mean is given .

So, we need to find the total sum of the marks of all 30 students .

This can be found by using a formula,

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

Using this we can find the sum of the marks obtained by all 300 students .

Now consider Statement - 2

Mean marks of top 100 students is 80 .

Here, Mean is given .

So, using the above mentioned formula find the sum of the marks obtained by top 100 students .

Then consider Statement - 3

Mean marks of last 100 students is 50 .

Here, mean is given .

So, using the above mentioned formula find the sum of marks obtained by last 100 students.

However,

No. of students left = 100.

Sum of the marks of remaining students = Total sum of the marks - Sum of the marks obtained by Top 100 students and last 100 students .

Hence;

From the above we can find the sum of the marks of remaining students.

Now , here sum is found .

So, we need to calculate the mean .

For this we need to use an formula,

The formula is ,

$\green{\boxed{\tt{Mean \; = \; \dfrac{Sum\;of\;the\;observations}{No. \; of \; observations}}}}$

Hence,

The mean of remaining students is found .

So, question is solved .

This is the explanation part . Below is the solution .

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Solution :

❶

Mean marks of all 300 students = 60

No. of students = 300

Sum of the marks = ?

$\longrightarrow{\tt{60 \times 300}}$

$\implies{\tt{18,000}}$

❷

Mean marks of top 100 students = 80

No. of students = 100

Sum of the marks = ?

$\longrightarrow{\tt{80\times 100}}$

$\implies{\tt{8 ,000}}$

❸

Mean marks of last 100 students = 50

No. of students = 100

Sum of the marks = ?

$\longrightarrow{\tt{50 \times 100}}$

$\implies{\tt{5,000}}$

Sum of marks of remaining students = ?

Sum of marks of all students - Sum of marks of top 100 students and last 100 students .

= 18,000 - 8,000 + 5,000

= 18,000 - 13,000

= 5,000

So,

Sum of marks of remaining 100 students = 5,000

No. of students = 50 .

Mean of marks of remaining 100 students = ?

= 5000/10

= 50

correct option - 4

$\blue{\boxed{\tt{Mean\;of\;marks\;of\;remaining\;students\;=\;50}}}$

$\red{\boxed{\tt{\therefore{Option\;-\;4\;is\;Correct}}}}$

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✔ Hence Solved .