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example of medianfor the vector 1 4 5 9 12 33 the median is the average of the 5 amp 9 in the middlegtgt median1 4 5 9 12 33ans
medianthe median is defined only for a data set which has been sorted first that means that the values are in order the median of a sorted set of
example of modewhen no value appears more often than any other the smallest value in the vector will be the mode of the vectorgtgt shortx 2 5 1
illustration of modewhen there is more than one value with similar highest frequency then the smaller value is mode in the case below as 3 and 8
modethe mode of a data set is the value which appears most often the built-in function in a matlab for this is known as the modegtgt x 9 10 10 9 8 7
illustration of standard deviationthe less spread out the numbers are therefore smaller the standard deviation will be as it is a way of determining
illustration of variancefor illustration for the vector 4 6 1 5 there are n 4 values therefore n - 1 is 3 the mean of this data set is also 4 the
find minimum and maximum for each rowto find the maximum or minimum for each row the dimension of 2 that is how a matlab refers to rows can be
example of minimum and maximum valuefor matrices the functions min and max operate column wise by the defaultgtgt mat randint241 20mat
illustration of minimum and maximum valueboth of these functions also return the index of the minimum or maximum value when there is more than one
minimum and maximum valuethe matlab has built-in functions for numerous statistics for illustration min and max to find the minimum or maximum value
statisticsthere are numerous statistical analyses which can be executed on data sets in matlab software the statistical functions are in the data
structure consisting of the fieldsa matlab can also solve the sets of equations in this illustration the solutions for x y amp z are returned as a
example of symbolic expressionwhen there is more than one variable the matlab selects which to solve for in the illustration below the equation ax2
symbolic expressionthe solve function solves an equation and returns the solutions as symbolic expressions the answer can be converted to numbers by
illustration of gauss-jordanheres an illustration of performing such substitutions by using matlabgtgt a 1 3 0 2 1 3 4 2 3a 1 3 02 1 34 2 3gtgt b 1
function numdenthe function numden will return individually the numerator amp denominator of a symbolic expressiongtgt sym13 12ans 56gtgt n d
expanding a functionthe expand function will multiply out terms and factor will do the oppositegtgt expandx2x-1ans x2 x-2gtgt factoransans x
simplification functionsthere are numerous functions which work with expressions and simplify the terms not all the expressions can be simplified but
illustration of symbolic variablewhen on the other hand z is a symbolic variable to start with quotes are not required around the expression and the
basic mathematical operationsall the basic mathematical operations can be executed on symbolic expressions and variables example add raise to a power
symbolic variables and expressionsthe matlab has a type known as sym for the symbolic variables and expressions these work with strings the
gauss-jordanthe gauss-jordan elimination technique begins in similar way which the gauss elimination technique does but then rather than of
gauss eliminationthe gauss elimination technique consists of generating the augmented matrix a b applying eros to augmented matrix to
replacement replace a row by adding it to or subtract from it a multiple of the other row for a given row ri this is written as ri - srj