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Chapter 25: Statistics 203var (x)Function FileFor vector arguments, return the (real) variance of the values. For matrix arguments,return a row vector contaning the variance for each column.The argument opt determines the type of normalization to use. Valid values are0: normalizes with N-1, provides the square root of best unbiased estimatorof the variance [default]1: normalizes with N, this provides the square root of the second momentaround the meanThe third argument dim determines the dimension along which the variance is calculated.[t, l x] = table (x)Function File[t, l x, l y] = table (x, y)Function FileCreate a contingency table t from data vectors. The l vectors are the correspondinglevels.Currently, only 1- and 2-dimensional tables are supported.studentize (x, dim)Function FileIf x is a vector, subtract its mean and divide by its standard deviation.If x is a matrix, do the above along the first non-singleton dimension. If the optionalargument dim is given then operate along this dimension.statistics (x)Function FileIf x is a matrix, return a matrix with the minimum, first quartile, median, thirdquartile, maximum, mean, standard deviation, skewness and kurtosis of the columnsof x as its rows.If x is a vector, treat it as a column vector.spearman (x, y)Function FileCompute Spearman’s rank correlation coefficient rho for each of the variables specifiedby the input arguments.For matrices, each row is an observation and each column a variable; vectors arealways observations and may be row or column vectors.spearman (x) is equivalent to spearman (x, x).For two data vectors x and y, Spearman’s rho is the correlation of the ranks of x andy.If x and y are drawn from independent distributions, rho has zero mean and variance1 / (n - 1), and is asymptotically normally distributed.run count (x, n)Function FileCount the upward runs along the first non-singleton dimension of x of length 1, 2,..., n-1 and greater than or equal to n. If the optional argument dim is given operatealong this dimension