Final answer:
The Cumulative sum (CUSUM) is used for monitoring shifts in data over time and assessing deviations from a central tendency.
Step-by-step explanation:
The Cumulative sum (CUSUM) is a method used in statistics to monitor the cumulative relative frequency or cumulative changes in data over time. In an ordered set of observations, the cumulative relative frequency is the sum of the relative frequencies for all values that are less than or equal to a given value. This technique is utilized to assess shifts in the central tendency of a production process or other applications where it is critical to detect changes relative to a target value or previous performance. It cumulates relative frequencies in statistics and can also apply to fields such as economics and biology for analyzing income distribution or postsynaptic potential changes.
As an example, consider the distribution of income across a population. The cumulative income distribution can be represented by summing the shares of income received by different segments of the population (e.g., quintiles). The bottom 40% of the population's income would be the total income of the first and second quintile. This continues such that the cumulative income must reach 100% when considering the entire population, as everyone cumulatively receives all the income.