Question

The arithmetic mean X of numbers 2, 3, 4, 1, 5, 7 is equal to their sum divided by the number of quantities. Frame a formula.
A. \[X=\dfrac{2+3+4+1+5+7}{8}\]
B. \[X=\dfrac{2+3+4+1+5+7}{3}\]
C. \[X=\dfrac{2+3+4+1+5+7}{6}\]
D. \[X=\dfrac{3+4+1+5+7}{6}\]

Answer 1

HINT:-
Before solving this question, we must know about Arithmetic Meaning.
ARITHMETIC MEAN: The arithmetic mean is the simplest way to measure the mean, or average of any group of numbers. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
The formula used to calculate the arithmetic mean, i.e. the average of numbers is written as follows:-
ARITHMETIC MEAN/AVERAGE $=\dfrac{Sum\text{ }of\text{ }all\text{ }the\text{ }numbers\text{ }in\text{ }the\text{ }series}{Count\text{ }of\text{ }the\text{ }numbers\text{ }used\text{ }in\text{ }the\text{ }series}$ .

Complete step by step answer:
Let us now solve this question.
As mentioned in the hint provided above, the formula to calculate arithmetic mean is given below:-
$=\dfrac{Sum\text{ }of\text{ }all\text{ }the\text{ }numbers\text{ }in\text{ }the\text{ }series}{Count\text{ }of\text{ }the\text{ }numbers\text{ }used\text{ }in\text{ }the\text{ }series}$
So, if the Arithmetic mean of the numbers 2, 3, 4, 1, 5, 7 is ‘X’, then, we can write this as follows:-
\[X=\dfrac{2+3+4+1+5+7}{6}\] .
And, the only option that matches with the explanation given above is option (c)\[X=\dfrac{2+3+4+1+5+7}{6}\] .
Hence, option (c) is the correct option.
NOTE:-
One must do all the calculations in this question very carefully.
Also not only in this question, the students must be very careful while solving any such questions as if there is any mistake in the calculus, then the answer can come out to be wrong.