Question

What is the average of 75 and 105?

Answer 1

Hint: We shall explain the concept of mean or average in order to solve this sum. Average for a set of numbers is nothing but the mean which can be calculated by adding all the terms in the set of data and dividing it by the total number of terms in the data set. Using this concept, we calculate the average for the given numbers 75 and 105.

Complete step by step solution:
In order to solve this question, let us first give the formula to calculate the average of two numbers. Average or mean of two numbers is nothing but the sum of the two numbers divided by the number of terms which is 2 in this case. Let us assume the two numbers are a and b. The average of the two numbers can be calculated as follows,
$ \text{Average=}\dfrac{a+b}{2}$
Using the above formula, we need to calculate the average for the two numbers 75 and 105. Substituting for a and b in the formula as 75 and 105, we get the average of the two numbers.
$\Rightarrow \text{Average=}\dfrac{75+105}{2}$
Adding the two terms in the numerator,
$\Rightarrow \text{Average=}\dfrac{180}{2}$
Dividing 180 by 2 we get,
$\Rightarrow \text{Average=90}$
Hence, the average of the two numbers 75 and 105 is 90.

Note: We need to note that the average of two numbers lets us calculate a number exactly in the middle of the two numbers. This means that the average number is in between the two said numbers such that it is equidistant from the two numbers. The difference between the average and the first number is the same as the difference between the second number and the average.