# Median Calculator

## Calculate medians step by step

The calculator will find the median ($$$50$$$^{th} percentile, second quartile) for the given sample data, with steps shown.

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### Your Input

**Find the median (percentile no. $$$50$$$) of $$$10$$$, $$$5$$$, $$$0$$$, $$$1$$$, $$$5$$$, $$$9$$$, $$$-3$$$, $$$2$$$.**

### Solution

The first step is to sort the values.

The sorted values are $$$-3$$$, $$$0$$$, $$$1$$$, $$$2$$$, $$$5$$$, $$$5$$$, $$$9$$$, $$$10$$$.

Next, the median value depends on the number of values. If the number of values is odd, the median is the "central" value among the sorted values. If the number of values is even, the median is the average of the two "central values".

We have $$$8$$$ values, so their number is even.

Since the number is even, the median is the average of the "central values": $$$-3$$$, $$$0$$$, $$$1$$$, $$${\color{red}2}$$$, $$${\color{red}5}$$$, $$$5$$$, $$$9$$$, $$$10$$$.

Calculate the median: $$$m = \frac{2 + 5}{2} = \frac{7}{2}$$$.

So, the median is $$$\frac{7}{2}$$$.