Provide an example where the outlier is more important to the research than the other observations?

Analysis of a spectrograph, where we measure amplitude or intensity of light as it varies with frequency. A spike (high amplitude or intensity for a particular frequency) has greater significance than the more level variation of amplitude for most other frequencies. It would indicates that something special is going on at or around a particular frequency and would encourage the researcher to focus more on the anomaly.

Subtracting is the opposite of adding