1. What is the Modified Z Score?

The Modified Z Score is a robust statistical measure used to identify outliers in a dataset. It uses median and median absolute deviation (MAD) instead of mean and standard deviation, making it less sensitive to extreme values.

2. How Does the Calculator Work?

The calculator uses the Modified Z Score equation:

Where:

• \( x \) — Individual data value
• \( \text{median} \) — Median of the dataset
• \( \text{MAD} \) — Median Absolute Deviation
• 0.6745 — Constant scaling factor

Explanation: The constant 0.6745 makes the MAD comparable to the standard deviation for normally distributed data. Values with |Z_mod| > 3.5 are typically considered outliers.

3. Importance of Modified Z Score Calculation

Details: The Modified Z Score is particularly useful in outlier detection when data may contain extreme values that would distort traditional z-scores based on mean and standard deviation.

4. Using the Calculator

Tips: Enter the data value (x), median of the dataset, and median absolute deviation (MAD). MAD must be greater than 0 for the calculation to be valid.

5. Frequently Asked Questions (FAQ)

Q1: Why use Modified Z Score instead of standard z-score?
A: Modified Z Score is more robust to outliers since it uses median and MAD instead of mean and standard deviation, which can be heavily influenced by extreme values.

Q2: What is considered an outlier using Modified Z Score?
A: Typically, values with |Z_mod| > 3.5 are considered potential outliers, though this threshold may vary depending on the specific application.

Q3: How is MAD calculated?
A: MAD = median(|x_i - median(X)|) where X is the entire dataset. It's the median of absolute deviations from the dataset's median.

Q4: When should I use Modified Z Score?
A: Use it when your data may contain outliers that could distort traditional statistical measures, or when working with non-normal distributions.

Q5: What does the constant 0.6745 represent?
A: This constant scales the MAD to be approximately equal to the standard deviation for normally distributed data, making the Modified Z Score comparable to the standard z-score.