Cumulative Average Calculator

Given a list of sequential data, you can find the cumulative moving average (or cumulative rolling average) by computing the average of all the data points up to the current point. For example, if you have the ordered data set

1, 3, 8, 12, 10, 8, 7, 15,

then the cumulative moving average is

1, 2, 4, 6, 6.8, 7, 7, 8

Cumulative moving averages are often used alongside simple n-point moving averages to compare various ways of smoothing raw data. The first entry in the cumulative moving average sequence is always the first data point. The second term in the c.m.a. is the average of the first two data points, etc. The last entry of the c.m.a. is the average of the entire data sequence. You can use the calculator below to find the cumulative moving average of a data set.

Recursive Equation and Number of Terms in the C.M.A.

The number of terms in the cumulative moving average is always equal to the number of data points in the original set. If the original set of ordered data is {x₁, x_n, ..., x_n} and the cumulative moving average sequence is {C₁, C₂, ..., C_n} then C_k is defined recursively as follows:

C_k+1 = (x_k+1 + k*C_k)/(k + 1).

In this type of cumulative moving average, all terms are weighted equally. However, you can also calculate weighted cumulative averages in which more recent terms are given greater weight than older data points. See also the calculators for linear, quadratic, and cubic weighted cumulative averages, as well as the exponential moving average.

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