The average of all the perfect squares up to $100$ is?

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Solution

Step 1: Find the sum of the numbers :
We have,
The perfect square numbers from $1$ to $100$ are, $1, 4, 9, 16, 25, 36, 49, 64, 81$ and $100$
So,
The sum of these numbers is given by $1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385 .$
Step 2: find the average :
Thus, The average of all the perfect square numbers from $1$ to $100$ is
$\begin{array}{rcl} A v e r a g e & = & \frac{t o t a l s u m}{t o t a l n u m b e r s} \\ = & \frac{385}{10} \\ = & 38.5 \end{array}$
Hence, The average of all the perfect square numbers from $1$ to $100$ is $38.5$

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