Statistic

Statistic library for Arduino includes sum, average, variance and std deviation

Description

The statistic library is made to get basic statistical information from a one dimensional set of data, e.g. a stream of values of a sensor.

The stability of the formulas is improved by the help of Gil Ross (Thanks!)

The functions implemented are:

• clear(useStdDev)
• add(value)
• count() returns zero if count == zero (of course)
• sum() returns zero if count == zero
• minimum() returns zero if count == zero
• maximum() returns zero if count == zero
• average() returns NAN if count == zero

These three functions only work id useStdDev == true:

• variance() returns NAN if count == zero
• pop_stdev() population stdev, returns NAN if count == zero
• unbiased_stdev() returnsNAN if count == zero

Operational

See examples

FAQ

Q: Are individual samples still available?

The values added to the library are not stored in the lib as it would use lots of memory quite fast. Instead a few calculated values are kept to be able to calculate the most important statistics.

Q: How many samples can the lib hold? (internal variables and overflow)

The counter of samples is an uint32_t, implying a maximum of about 4 billion samples. In practice 'strange' things might happen before this number is reached. There are two internal variables, _sum which is the sum of the values and _ssq which is the sum of the squared values. Both can overflow especially _ssq can and probably will grow fast. The library does not protect against it.

There is a workaround for this (to some extend) if one knows the approx average of the samples before. Before adding values to the lib subtract the expected average. The sum of the samples would move to around zero. This workaround has no influence on the standard deviation.

!! Do not forget to add the expected average to the calculated average.

(Q: should this subtraction trick be build into the lib?)

Q: How about the precision of the library?

The precision of the internal variables is restricted due to the fact that they are 32 bit float (IEEE754). If the internal variable _sum has a large value, adding relative small values to the dataset wouldn't change its value any more. Same is true for _ssq. One might argue that statistically speaking these values are less significant, but in fact it is wrong.

There is a workaround for this (to some extend). If one has the samples in an array or on disk, one can sort the samples in increasing order (abs value) and add them from this sorted list. This will minimize the error, but it works only if the samples are available and the they may be added in the sorted increasing order.

Q: When will internal var's overflow? esp. squared sum

IEEE754 floats have a max value of about +-3.4028235E+38

Q: Why are there two functions for stdev?

There are two stdev functions the population stdev and the unbiased stdev. See Wikipedia for an elaborate description of the difference between these two.