The Modified Z-score applies the median calculation instead of the mean. Furthermore, the signed number of standard deviations is replaced by the Mean Absolute Deviation (around the Median).

### Indicator Description

A standard Z-score reveals how far removed a data point is from the mean, measured in standard deviations. The modified Z-score applies the median whereas the standard deviations has been replaced by the Mean Absolute Deviation (around the Median).

For a normally distributed sample, 95.8% of the Z-scores of all data points fall within the range [-2, +2]. A Z-score of 0 indicates that the data point is identical with the arithmetic mean of the data set.

The modified Z-score is a normalized oscillator and can be used to identify extreme readings of the input series. The modified Z-score is calculated by dividing the absolute difference between a data point and the median by the Mean Absolute Deviation (around the Median).

One of the main applications of the indicator is that it can be used to normalize any oscillator. For example, the MACD is a non normalized oscillator which does not pass the c-test introduced by William Eckhardt. When the Z-score is used to normalize the MACD, the resulting oscillator uses a normalized scale and will pass the c-test. The normalized MACD is obtained, when the MACD is used as the input series for the modified Z-score.

More information on the process of normalization and the Z-score was discussed in our Indicator Spotlight.

#### Other Library Indicators

You may want to review other indicators in the Multi Points Statistics category, featuring the Moving Mean TPO, Moving Mean VWTPO, Moving MedianTPO, Moving Median VWTPO, Moving Mode TPO and the Moving Mode VWTPO.

You may want to review other indicators in Statistical Analysis category, including the Mean Absolute Deviation (around the Mean and Median), the Moving Median, the Median Absolute Deviation (around the Median), the Standard Deviation, Volume Weighted Standard Deviation, the Volume Weighted Mean Absolute Deviation and the Interquartile Range indicator. Finally, this category also contains the Standard Z Score indicator.

The most frequently used institutional price benchmark to establish the Volume Weighted Average Price was discussed in our Indicator Spotlight.

The indicator is available for NinjaTrader 8.