This chapter lists and describes many of Mathcad’s built-in statistical functions. These functions perform a wide variety of computational tasks, including statistical analysis, interpolation, regression, and smoothing.

The following sections make up this chapter:

**Population and sample statistics**

Functions for computing the mean, variance, standard deviation, and correlation of data.

**Probability distributions**

Functions for evaluating probability densities, cumulative probability distributions and their inverses for over a dozen common distribution functions.

**Histogram function**

now to count the number of data values falling into specified intervals.

**Random numbers**

Generating random numbers having various distributions.

**Interpolation and prediction functions**

Linear and cubic spline interpolation. Functions for multivariate interpolation.

**Regression functions**

Functions for linear regression, polynomial regression, and regression using combinations of arbitrary functions.

**Smoothing functions**

Functions for smoothing time series with either a running median, a Gaussian kernel, or an adaptive linear least-squares method.

**Population and sample statistics**

Mathcad includes eight functions for population and sample statistics. In the following descriptions, m and n represent the number of rows and columns in the pecified arrays. In the formulas below, the built-in variable ORIGIN is set to its default value of zero.

**Probability distributions**

Mathcad includes several functions for working with several common probability densities. These functions fall into three classes:

Probability densities: These give the likelihood that a random variable will take on a particular value.

Cumulative probability distributions: These give the probability that a random variable will take on a value less than or equal to a specified value. These are obtained by simply integrating (or summing when appropriate) the corresponding probability density over an appropriate range.

Inverse cumulative probability distributions: These functions take a probability as an argument and return a value such that the probability that a random variable will be less than or equal to that value is whatever probability you supplied as an argument.

**Probability densities**

These functions return the likelihood that a random variable will take on a particular value. The probability density functions are the derivatives of the corresponding cumulative distribution functions discussed in the next section.

Returns the probability density for the beta distribution:

Return P(X = k) when the random variable X has the binomial

**Cumulative probability distributions**

These functions return the probability that a random variable is less than or equal to a specified value. The cumulative probability distribution is simply the probability density function integrated from -00 to the specified value. For integer random variables, the integral is replaced by a summation over the appropriate range.

The probability density functions corresponding to each of the following cumulative distributions are given in the section “Probability distributions” on page 281. Figure 14-1 at the end of this section illustrates the relationship between these three .A functions.

**Inverse cumulative probability distributions**

These functions take a probability p as an argument and return the value of x such that P(X::;x) = p.

The probability density functions corresponding to each of the following inverse cumulative distributions are given in the section “Probability distributions;’ on page 281.