Question

Find the arithmetic mean between 24 and 36.
\[\begin{align}
  & \text{(A) 26} \\
 & \text{(B) 28} \\
 & \text{(C) 30} \\
 & \text{(D) 32} \\
\end{align}\]

Answer 1

Hint: First of all, we should know the definition of arithmetic mean. The average of two numbers is said to be the arithmetic mean of two numbers. We know that the ratio of sum of numbers to the total numbers is equal to the average of two numbers. So, let us assume x as 24 and y as 36. Now we will find the sum of x and y. Now we will divide the sum of x and y with 2. This will give the arithmetic mean between 24 and 36.

Complete step-by-step answer:
Before solving the question, we should know the definition of arithmetic mean. The average of two numbers is said to be the arithmetic mean of two numbers. Let us assume two numbers x and y. The sum of two numbers is equal to x + y. We know that the ratio of sum of numbers to the total numbers is equal to the average of two numbers. So, the average of two numbers x and y is equal to the sum of x and y and 2.
So,
\[\text{Average of x and y}=\dfrac{\text{Sum of x and y}}{2}=\dfrac{x+y}{2}\]
We know that the average of two numbers gives us an arithmetic mean of two numbers. So, the average of x and y gives us the arithmetic mean of x and y.
\[\text{Arithmetic Mean of x and y}=\dfrac{\text{Sum of x and y}}{2}=\dfrac{x+y}{2}\]
In the question, we were asked to find the arithmetic mean of 24 and 36.
Let us assume the value of x as 24 and the value of y as 36.
Sum of x and y \[=x+y=24+36=60\]
We know that the ratio of sum of numbers and number of numbers give the average of those numbers.
So,
\[\text{Average of x and y}=\dfrac{\text{Sum of x and y}}{2}=\dfrac{x+y}{2}=\dfrac{60}{2}=30\]
So, the average of 24 and 36 is equal to 30.
We know that the arithmetic mean of two numbers is equal to the average of two numbers.
Hence, the arithmetic mean of 24 and 36 is equal to 30.

Note: Let us assume the arithmetic mean of \[{{x}_{1}},{{x}_{2}},....{{x}_{n}}\] is equal to \[\bar{X}\]. We know that arithmetic mean is the ratio of sum of numbers and number of numbers. So, the sum of \[{{x}_{1}},{{x}_{2}},....{{x}_{n}}\] is equal to \[{{x}_{1}}+{{x}_{2}}+.....+{{x}_{n}}\]. We are having n numbers in \[{{x}_{1}},{{x}_{2}},....{{x}_{n}}\]. Then \[\bar{X}=\dfrac{{{x}_{1}}+{{x}_{2}}+.....+{{x}_{n}}}{n}=\dfrac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}}\]. By using this formula, we can find the arithmetic mean of \[{{x}_{1}},{{x}_{2}},....{{x}_{n}}\].