Median

The median is the middle value when data is sorted.

Median

The median is the middle value when the values are sorted; with an even count it is the mean of the two middle ones.

x = np.array([3, 1, 100, 2, 4])
print(np.median(x))   # 3.0   sorted: 1 2 3 4 100
print(x.mean())       # 22.0

The median isn't affected by outliers; for skewed distributions like income or house prices it is better than the mean as a "typical value".

Percentiles and mode

The median is the 50th percentile. Other percentiles describe the shape of the distribution:

x = np.arange(1, 101)
print(np.percentile(x, [25, 50, 75]))   # [25.75 50.5  75.25]

vals, counts = np.unique([2, 3, 3, 5, 3], return_counts=True)
print(vals[counts.argmax()])            # 3  (mode: most frequent value)

The mode is used to fill missing values in categorical data (strategy="most_frequent").

Exercise Outlier-robust centre

Print the mean and the median of the gelir array separated by a space; see the difference.

Show example solution

import numpy as np

gelir = np.array([20, 22, 25, 23, 210])

print(gelir.mean(), np.median(gelir))

Test yourself

What is <code>np.median([5, 1, 3, 7])</code>?
- 4.0
- 3.0
- 5.0
- 4.5
Show answer

4.0 — Sorted: 1 3 5 7; the mean of the middle two (3 and 5) is 4.
Compute the median.
```
m = np.____(x)
```
Show answer
```
m = np.median(x)
```
Match the measures.

mean

Sum / count
median

Middle sorted value
mode

Most frequent value
75th percentile

Upper quartile boundary

Next lesson: Standard deviation

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