The mean is the arithmetic average of a set of values, the sum divided by the count. For values :
The mean is the first moment of the distribution. It tells you where the values are centered, in the same units as the data itself.
In Feature extraction from a signal, the rolling mean within a window is one of the most basic features. For an ECG window containing one heartbeat, the mean is the average voltage: close to zero for a centered signal, a small positive number for an uncentered one. The mean captures the baseline level of the signal in that window.
In Normalization, the mean is subtracted from each value to produce a zero-mean signal, the first step in computing the z-score.
For higher moments that describe more of the distribution’s shape:
- Variance (second moment): how spread out the values are. Its square root is the Standard deviation.
- Skewness (third moment): asymmetry. Positive skew means a long right tail; negative skew means a long left tail.
- Kurtosis (fourth moment): tail heaviness. How prone the distribution is to extreme values.
The first four moments are a compact summary of a distribution’s shape. They’re the standard feature set for windowed analysis of signals.
The mean is computed in Pandas with df['col'].mean() (over the whole column) or df['col'].rolling(N).mean() (over a sliding window). In NumPy it’s np.mean(arr).
The arithmetic mean is one of several notions of average. The median (middle value) and mode (most common value) are alternatives that behave differently for skewed distributions. For a perfectly symmetric distribution, mean = median = mode. For a positively skewed distribution, mean > median > mode. For a negatively skewed distribution, the order reverses.