# mad

Return the Median Absolute Deviation (MAD) of the value of the specified field.

```
put|reduce mad(field)
```

Parameter | Description | Required? |
---|---|---|

`field` |
The field to compute | Yes |

Median Absolute Deviation (MAD) is related to standard deviation in much
the way that median is related to mean. It is a robust measure of how
spread out a set of values are around their central location (the
median). `MAD = median( | x - median| )`

*Example: MAD and standard deviations*

The example below shows how MAD and standard deviation behave on samples from a pure normal distribution and samples from a distribution "contaminated" with an outlier distribution (1% contamination). The MAD estimate for the contaminated distribution remains close to its value for the dominant (pure) distribution, unlike the standard deviation.

This example uses a module from the standard library.

```
import "random.juttle" as random;
emit -limit 1000 -from Date.new(0)
| put pure = random.normal(0, 1)
| put mixed = (Math.random() < .99) ? random.normal(0, 1) : random.normal(100, 0.1)
| reduce
pure_mean = avg(pure),
pure_median = percentile(pure, 0.5),
pure_sd = stdev(pure),
pure_mad = mad(pure) * 1.48, // the 1.48 factor scales normal MAD to be same as normal SD
mixed_mean = avg(mixed),
mixed_median = percentile(mixed, 0.5),
mixed_sd = stdev(mixed),
mixed_mad = mad(mixed) * 1.48
| view table -columnOrder ['pure_mean', 'pure_sd', 'pure_median', 'pure_mad', 'mixed_mean', 'mixed_sd', 'mixed_median', 'mixed_mad']
```