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In this lesson, you will learn how to find the median of a dataset by hand, and using Python's NumPy. 

We will also discuss the strengths and limitations of using median as a descriptive statistic of a dataset.

Median

The formal definition for the median of a dataset is:

*The value that, assuming the dataset is ordered from smallest to largest, falls in the middle. If there are an even number of values in a dataset, you either report both of the middle two values or their average.*

There are always two steps to finding the median of a dataset:
1. Order the values in the dataset from smallest to largest
2. Identify the number(s) that fall(s) in the middle 

#### Example One: Even Number of Values

Say we have a dataset with the following ten numbers: 
```tex
24,\ 16,\ 30,\ 10,\ 12,\ 28,\ 38,\ 2,\ 4,\ 36
```

The first step is to order these numbers from smallest to largest:

```tex
2,\ 4,\ 10,\ 12,\ [16,\ 24],\ 28,\ 30,\ 36,\ 38
```

Because this dataset has an even number of values, there are two medians: `16` and `24` &mdash; `16` has four datapoints to the left, and `24` has four datapoints to the right.        

Although you can report both values as the median, people often average them. If you averaged `16` and `24`, you could report the median as `20`.

#### Example Two: Odd Number of Values

If we added another value (say, `24`) to the dataset and sorted it, we would have: 
```tex
2,\ 4,\ 10,\ 12,\ 16,\ [24],\ 24,\ 28,\ 30,\ 36,\ 38
```
The new median is equal to `24`, because there are 5 values to the left of it, and 5 values to the right of it.


In this lesson, you learned how to find the median of a dataset in two steps:
1. Sort the dataset
2. Identify the one or two numbers that fall in the middle of the sorted dataset

You also learned how to calculate the median using NumPy:
```py
np.median(my_array)
```

#### Discussion

Take a look at the histogram to the right. It displays the author age distribution with vertical lines for the mean (red) and median (yellow).

Do you feel like the median of our dataset, 40.5, provides us enough information to claim when authors publish their greatest work?

We argue it does not.

Although the median is a good measure of the dataset's center, we cannot make a definitive claim about when authors publish their greatest work &mdash; the youngest author published at 18 and the oldest at 76. It would be irresponsible to say anything but, "it seems to be possible at almost any age."

Notice that the mean and the median are nearly equal. This is not a surprising result, as both statistics are a measure of the dataset's center. However, it's worth noting that these results will not always be so close.

In the instructions below, we've written a brief explanation that puts median in the context of our problem.

Review and Discussion

In this lesson, you will learn how to find the *median* of a dataset &mdash; a common measure of a dataset's center. Each of the next three exercises will cover the following topics:
- Manually finding the median of a dataset
- Using Python's NumPy library to find the median of a dataset
- Interpreting what it means for a dataset to have similar and different median and mean values

In the lesson, we will use a dataset of the 100 greatest novels, determined by a French literary magazine, Le Monde. From the dataset, you will use the median to answer the question: 

*When are great authors most likely to publish their best work?*

If you are not familiar with mean, also known as average, we recommend that you learn about it in our lesson on <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/average/exercises/introduction" target="_blank">average</a>.




Introduction

Finding the median of a dataset becomes increasingly time-consuming as the size of your dataset increases &mdash; imagine finding the median of an unsorted dataset with 10,000 observations.

The NumPy `.median()` function can do the work of sorting, then finding the median for you. In the example below, we use `np.median()` to calculate the median of a dataset with ten values:

```py
example_array = np.array([24, 16, 30, 10, 12, 28, 38, 2, 4, 36, 42])

example_median = np.median(example_array)

print(example_median)
```

The code above prints the median of the dataset, `24`. The mean of this dataset is `22`. It's worth noting these two values are close to one another, but not equal.
