Modified Z Score Calculator

Formula

The formula to calculate the modified Z score is:

\[ Z = 0.6745 \times \frac{X - M}{MAD} \]

Where:

\( Z \) is the modified Z score
\( X \) is the observation
\( M \) is the median
\( MAD \) is the median absolute deviation

What is a Modified Z Score?

A modified Z score is a statistical measure that indicates how many median absolute deviations (MAD) an observation is away from the median of a dataset. Unlike the traditional Z score, which uses the mean and standard deviation, the modified Z score uses the median and MAD, making it more robust to outliers. This measure is particularly useful in identifying outliers in a dataset, as it provides a more accurate representation of the data’s central tendency and variability.

Example Calculation

Let's assume the following values:

Observation (X) = 10
Median (M) = 5
Median Absolute Deviation (MAD) = 2

Using the formula to calculate the modified Z score:

\[ Z = 0.6745 \times \frac{10 - 5}{2} = 1.69 \]

The modified Z score is 1.69.