Answer

Verified

406.2k+ views

Hint: Arithmetic mean is calculated by adding the values of all the terms and dividing the sum by the total number of terms.

The arithmetic mean of numbers a, b, c, d, e is given to us as M. So, here it has been given the mean of five terms.

We know that the arithmetic mean is calculated by adding the value of all the terms and dividing the sum by the total number of terms. i.e. $=\dfrac{\sum\limits_{i=1}^{i=n}{{{x}_{i}}}}{n}$ .

The arithmetic mean is also known as the average number.

The arithmetic mean is used mostly in mathematics and statistics but it has some uses in the field of economics, anthropology, and history also.

Here in the question, arithmetic mean is given to us and we know that the total number of terms is 5.

So,

$\dfrac{a+b+c+d+e}{5}=M$

Now multiplying by $5$ on both sides of the equation.

$a+b+c+d+e=5M....\left( i \right)$

Now we need to find $(a-M)+(b-M)+(c-M)+(d-M)+(e-M)$ so, we solve the equation and open the bracket and add or subtract the like terms in the equation. Like terms are those terms that have the same variable in the equation.

And now, we will get

$\begin{align}

& =(a-M)+(b-M)+(c-M)+(d-M)+(e-M) \\

& =a+b+c+d+e-5M \\

\end{align}$

Using equation (i).

We can substitute the value from equation (i) and we will get

$=5M-5M$

$=0$

So, $(a-M)+(b-M)+(c-M)+(d-M)+(e-M)=0$

Our answer after solving the equation is 0.

So, the correct option is c.

Note: The arithmetic mean is simply considered as a form of average. So mean and average are the same with the same formula. And remember in solving this type of question, we must first use the arithmetic formula to get an equation that can be substituted in $(a-M)+(b-M)+(c-M)+(d-M)+(e-M)$.

The arithmetic mean of numbers a, b, c, d, e is given to us as M. So, here it has been given the mean of five terms.

We know that the arithmetic mean is calculated by adding the value of all the terms and dividing the sum by the total number of terms. i.e. $=\dfrac{\sum\limits_{i=1}^{i=n}{{{x}_{i}}}}{n}$ .

The arithmetic mean is also known as the average number.

The arithmetic mean is used mostly in mathematics and statistics but it has some uses in the field of economics, anthropology, and history also.

Here in the question, arithmetic mean is given to us and we know that the total number of terms is 5.

So,

$\dfrac{a+b+c+d+e}{5}=M$

Now multiplying by $5$ on both sides of the equation.

$a+b+c+d+e=5M....\left( i \right)$

Now we need to find $(a-M)+(b-M)+(c-M)+(d-M)+(e-M)$ so, we solve the equation and open the bracket and add or subtract the like terms in the equation. Like terms are those terms that have the same variable in the equation.

And now, we will get

$\begin{align}

& =(a-M)+(b-M)+(c-M)+(d-M)+(e-M) \\

& =a+b+c+d+e-5M \\

\end{align}$

Using equation (i).

We can substitute the value from equation (i) and we will get

$=5M-5M$

$=0$

So, $(a-M)+(b-M)+(c-M)+(d-M)+(e-M)=0$

Our answer after solving the equation is 0.

So, the correct option is c.

Note: The arithmetic mean is simply considered as a form of average. So mean and average are the same with the same formula. And remember in solving this type of question, we must first use the arithmetic formula to get an equation that can be substituted in $(a-M)+(b-M)+(c-M)+(d-M)+(e-M)$.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Which neighbouring country does not share a boundary class 9 social science CBSE

The highest peak in Annamalai hills is aAnaimudi bDodabetta class 9 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which places in India experience sunrise first and class 9 social science CBSE

The highest peak of South India is A Doda Betta B Guru class 8 social science CBSE

Banaras Hindu University was founded by A CR Das B class 12 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which is the largest saltwater lake in India A Chilika class 8 social science CBSE