# Median

Median is a measure of central tendency -- it's a number that can summarize a set of data or a group of numbers.

If you think about driving, the median is the divider in the middle of the road. Likewise, the median of a set of data is the number in the middle.

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**How do you find a median?**

The first, and most critical step, is to put the numbers (or data points) in order from least to greatest. If you try to find the "middle number" before you put the numbers in order, it's like selecting a number at random!

So, if you have 5 test scores:

$79$, $81$, $83$, $70$, $95$

You need to put those in order from least to greatest:

$70$, $79$, $81$, $83$, $95$

Then, you find the number in the middle

$70$, $79$, $\underline{81}$, $83$, $95$

If you have a huge set of numbers, you can cross out the numbers from the front, then the back, one by one, until you are left with one number in the middle.

$\cancel{70}$, $\cancel{79}$, $\underline{81}$, $\cancel{83}$, $\cancel{95}$

The median of this set of numbers is: $81$

Finding medians is a tiny bit more complicated when you have an even number of datapoints in your data set.

Let's say you had on additional score in your set of test scores:

$79$, $81$, $83$, $70$, $95$, $88$

Put them in order:

$70$, $79$, $81$, $83$, $88$, $95$

But when you find the middle, you are left with two numbers in the middle:

$70$, $79$, $\underline{81}$, $\underline{83}$, $88$, $95$

When you have two numbers in the middle, the median is the average (or mean) of those two numbers. You can learn more about Averages in our Means Lesson. But, in thise case you will always be finding the mean of two numbers, so you add them together and divide by two:

$\dfrac{81+83}{2}=82$

The median of that set of numbers is $82$ (which, if you think about it, is the middle of that set of numbers, the middle just doesn't happen to be one of the datapoints).

#### Practice Problems:

## Median

1. $11, 96, 75, 83, 59, 51, 72, 34, 23$

2. $53, 89, 97, 64, 74, 20, 32, 85$

3. $50, 53, 35, 98, 39, 97, 33, 31, 95$

4. $60, 19, 64, 37, 81, 86, 45$

5. $38, 83, 34, 93, 17$

6. $11, 50, 67, 13, 54, 14, 13, 79$

7. $56, 45, 32, 95, 87, 53$

8. $83, 92, 12, 22, 51$

9. $85, 49, 55, 89, 27$

10. $83, 24, 84, 69, 75$

11. $99, 25, 30, 92, 54$

12. $27, 18, 26, 30, 15, 74$