Upgrading from:

Statistics`Common`

Functionality in this package has been added to the built‐in Mathematica kernel or incorporated into newly created packages.
CDF, PDF, and CharacteristicFunction are built into the kernel.
RandomArray is replaced by RandomReal and RandomInteger.
CovarianceMatrix and CorrelationMatrix are replaced by Covariance and Correlation for data.
RegionProbability is replaced by EllipsoidProbability.
New Hypothesis Testing and Multivariate Statistics packages have been created.

CDF, PDF, and CharacteristicFunction are built into the Mathematica kernel:

Version 5.2 << Statistics`NormalDistribution`; PDF[NormalDistribution[0, 1], x]

RandomArray is replaced by RandomReal for continuous distributions:

Version 5.2 << Statistics`ContinuousDistributions`; RandomArray[BetaDistribution[2, 3], 10]

RandomArray is replaced by RandomInteger for discrete distributions:

Version 5.2 << Statistics`DiscreteDistributions`; RandomArray[PoissonDistribution[5], 10]

Covariance matrix for data:

Version 5.2 << Statistics`MultiDescriptiveStatistics`; CovarianceMatrix[{{10, 50}, {10, 15}, {20, 25}, {10, 15}}]

RegionProbability is replaced by EllipsoidProbability:

Version 5.2 << Statistics`MultinormalDistribution`; ndist = MultinormalDistribution[{0, 0}, {{1, 1/3}, {1/3, 1}}]; ellipse = EllipsoidQuantile[ndist, .5]; RegionProbability[ndist, ellipse]
Hypothesis Testing Package

Symbols from Statistics`Common`PopulationsCommon` are now found in the Hypothesis Testing package:

EqualVariances KnownVariance

The KnownVariance option replaces KnownStandardDeviation:

Version 5.2 << Statistics`HypothesisTests`; MeanTest[{1, 4, 2, 5, 10}, 5, KnownStandardDeviation  2]