# Z-Score

A Z-score or standard score is a numerical measurement of a value’s relationship to the arithemic mean of the data set. A post discussing different applications of the indicator is available in our Spotlight on the

### Indicator Description

The Zscore indicator displays the signed number of standard deviations, i.e. showing whether a data point is above or below the mean value of the data set. The Z score indicator is therefore a normalized value and can be used to identify extreme readings from the input series. The Zscore indicator calculates by dividing the absolute difference between a data point and the arithmetic mean by the standard deviation.

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

One of the main applications of the Z Score 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. However, when the Z Score indicator 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 standard score.

For more information, you may review our indicator spotlight on the Z-score and normalization.

#### Other Library Indicators

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

Other indicators in the Statistical Analysis category, include the  Mean Absolute Deviation (around the Mean and Median), the Moving Median, the Median Absolute Deviation (around the Median), the Standard DeviationVolume Weighted Standard Deviation, the Volume Weighted Mean Absolute Deviation and the Interquartile Range indicator.

The library also contains a Modified Z Score. It 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).

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.