Modified Z Score Calculator

Enter the observation, median, and median absolute deviation (MAD) into the calculator to determine the modified Z score.

Modified Z Score Outlier Thresholds From Data IQR Method Compare Methods

Enter any 3 values to calculate the missing variable

Observation Median Median Absolute Deviation Modified Z Score Outlier threshold (|Z| ≥) Output decimals Outlier? Approx two-tailed p-value (normal assumption)

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Modified Z Score Formula

The following formula is used to calculate the modified Z score for a given observation.

Z = 0.6745 * (X - M) / MAD

Variables:

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

To calculate the modified Z score, subtract the median from the observation, divide the result by the median absolute deviation (MAD), and then multiply by 0.6745.

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.

How to Calculate Modified Z Score?

The following steps outline how to calculate the Modified Z Score.

First, determine the observation (X).
Next, determine the median (M) of the dataset.
Next, calculate the median absolute deviation (MAD).
Finally, calculate the Modified Z Score using the formula Z = 0.6745 * (X - M) / MAD.
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Observation (X) = 10

Median (M) = 5

Median Absolute Deviation (MAD) = 2