Question

The average of all the perfect squares upto 100 is:
a. 38.5
b. 1000
c. 100
d. 385

Answer 1

Hint:We will first list out all the perfect square numbers between 1 and 100. Then, we will find the average by using the formula, $\dfrac{\text{sum of all numbers}}{\text{total number of numbers}}$. For example, if we have 2 numbers, a and b, then the average of the two numbers is given by, $\dfrac{a+b}{2}$.

Complete step-by-step answer:
It is given in the question that we have to find the average of all the perfect squares upto 100. So, basically, a perfect square is a number from a given number system, which can be expressed as the square of a number from the same number system. For example, 4 is a perfect square.
Now, we will list out all the perfect squares and then find their sum by adding all the perfect squares upto 100. So, the perfect square numbers from 1 to 100 are, 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
On adding these numbers, we will get as follows,
1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385
Now, we have to find the average of these perfect numbers. So, we can find the average using the formula, $\dfrac{\text{sum of all numbers}}{\text{total number of numbers}}$.
We know that the sum of all the perfect square numbers is 385 and the number of perfect square numbers are 10. Hence, we can write the average of perfect square numbers as,
$\dfrac{385}{10}=38.5$
Thus, the average of all the perfect square numbers from 1 to 100 is 38.5. Hence, option (a) is the correct answer.

Note: The possible mistake that the students can make in this question, is by not considering 1 as a perfect square number. It is to be noted that 1 is also a perfect square number. Also, some students may make mistakes while doing the calculation. So, the students are recommended to solve the question carefully.