Find the Median 0 , 5*( square root of 2469)^2

$0$ , $5 \cdot {(\sqrt{2469})}^{2}$

Step 1

Arrange the terms in ascending order.

$0, 5 \cdot {(\sqrt{2469})}^{2}$

Step 2

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{0 + 5 \cdot {(\sqrt{2469})}^{2}}{2}$

Step 3

Remove parentheses.

$\frac{0 + 5 \cdot {(\sqrt{2469})}^{2}}{2}$

Step 4

Simplify the numerator.

Rewrite ${\sqrt{2469}}^{2}$ as $2469$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2469}$ as $2469^{\frac{1}{2}}$ .

$\frac{0 + 5 \cdot {(2469^{\frac{1}{2}})}^{2}}{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{0 + 5 \cdot 2469^{\frac{1}{2} \cdot 2}}{2}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{0 + 5 \cdot 2469^{\frac{2}{2}}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{0 + 5 \cdot 2469^{\frac{2}{2}}}{2}$

Rewrite the expression.

$\frac{0 + 5 \cdot 2469^{1}}{2}$

Evaluate the exponent.

$\frac{0 + 5 \cdot 2469}{2}$

Multiply $5$ by $2469$ .

$\frac{0 + 12345}{2}$

Add $0$ and $12345$ .

$\frac{12345}{2}$

Step 5

Convert the median $\frac{12345}{2}$ to decimal.

$6172.5$