To determine the median of all two-digit perfect squares, we'll follow a step-by-step process.
Here are the steps to find the median:
1. List the two-digit perfect squares: First, we need to identify all the perfect squares that are two-digit numbers. These numbers are:
- [tex]\(16\)[/tex] ([tex]\(4^2\)[/tex])
- [tex]\(25\)[/tex] ([tex]\(5^2\)[/tex])
- [tex]\(36\)[/tex] ([tex]\(6^2\)[/tex])
- [tex]\(49\)[/tex] ([tex]\(7^2\)[/tex])
- [tex]\(64\)[/tex] ([tex]\(8^2\)[/tex])
- [tex]\(81\)[/tex] ([tex]\(9^2\)[/tex])
2. Order the numbers: Next, we'll order these perfect squares in ascending order:
[tex]\[
16, 25, 36, 49, 64, 81
\][/tex]
3. Find the median: The median is the middle number in a sorted list of numbers. If the list has an even number of elements, the median will be the average of the two central numbers. Our list has six numbers (an even number), so we need to find the average of the third and fourth numbers:
[tex]\[
\text{Third number} = 36
\][/tex]
[tex]\[
\text{Fourth number} = 49
\][/tex]
To find the median, calculate the average of 36 and 49:
[tex]\[
\text{Median} = \frac{36 + 49}{2} = \frac{85}{2} = 42.5
\][/tex]
Therefore, the median of all two-digit perfect squares is:
[tex]\[
\boxed{42.5}
\][/tex]
So, the correct choice is:
[tex]\[
\text{E. } 42.5
\][/tex]
