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The formula to calculate the future value (F) of a particular amount (P), given a fixed interest rate (r) and a fixed number of years (n) is F = P(1 + r/100)n Performing the calculation in PHP is a simple matter of turning this formula into executable code Nevertheless, you d be surprised how many novice programmers forget all about PHP s operator precedence rules and, as a result, generate incorrect results The previous listing uses braces to correctly define the order in which the variables are processed
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216 Calculating Statistical Values
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You want to calculate statistical measures, such as variance or skewness, for a number set
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Use PEAR s Math_Stats class:
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< php // include Math_Stats class include "Math/Statsphp"; // initialize object $stats = new Math_Stats(); // define number series $series = array(76, 7348, 56, 26, 189, 6759, 17594, 2648, 192979, 54, 329, 820); // connect object to series $stats->setData($series); // calculate complete statistics $data = $stats->calcFull(); print_r($data); >
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PEAR s Math_Stats class, available from http://pearphpnet/package/Math_ Stats, is designed specifically to calculate statistical measures for a set of numbers This number set must be expressed as an array, and passed to the class setData() method The calcFull() method can then be used to generate a basic or expanded set of statistics about the number set The return value of this method is an associative array, with keys for each statistical measure calculated For example, the variable $data['median'] would return the median of the number set To get a better idea of the kind of analysis performed, consider the following output of the calcFull() method:
Array ( [min] => 26 [max] => 17594 [sum] => 3111398 [sum2] => 375110698612 [count] => 12 [mean] => 259283166667 [median] => 259 [mode] => Array ( [0] => 192979 [1] => 820 [2] => 2648 [3] => 7348 [4] => 17594 [5] => 329 [6] => 189 [7] => 54 [8] => 56 [9] => 6759 [10] => 76 [11] => 26 ) [midrange] => 87983 [geometric_mean] => 324444468821 [harmonic_mean] => 261106363977 [stdev] => 517368679862 [absdev] => 33019175 [variance] => 267670350902 [range] => 175914
2: Working with Numbers
[std_error_of_mean] => 149351473294 [skewness] => 202781206173 [kurtosis] => 298190358339 [coeff_of_variation] => 199538090541 [sample_central_moments] => Array ( [1] => 0 [2] => 245364488327 [3] => 280820044848 [4] => 42858793901E+015 [5] => 634511539688E+019 ) [sample_raw_moments] => Array ( [1] => 259283166667 [2] => 312592248844 [3] => 489107716046 [4] => 823326983124E+015 [5] => 142287015523E+020 ) [frequency] => Array ( [26] => 1 [54] => 1 [56] => 1 [6759] => 1 [76] => 1 [189] => 1 [329] => 1 [820] => 1 [192979] => 1 [2648] => 1 [7348] => 1 [17594] => 1 ) [quartiles] => Array ( [25] => 61795 [50] => 259 [75] => 2288895 )
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[interquartile_range] => 22271 [interquartile_mean] => 568563333333 [quartile_deviation] => 111355 [quartile_variation_coefficient] => 947423947862 [quartile_skewness_coefficient] => 0822904225226 )
As the previous listing illustrates, calcFull() generates a complete set of statistics about the data, including its mean, median, mode, and range; its variance and standard deviation; its skewness, kurtosis, and moments; and its quartiles, inter-quartile range, and quartile deviation Normally, you d need a fair bit of time with a calculator to calculate these values; the Math_Stats class generates them for you quickly and accurately It s also possible to generate a histogram and plot the frequency distribution of a data set, with PEAR s Math_Histogram package at http://pearphpnet/package/ Math_Histogram The following listing illustrates this:
< php // include Math_Histogram class include "Math/Histogramphp"; // define number series $series = array(10,73,27,11,92,97,49,86,92,4,32,61,2,13,48,81,94,17,8); // initialize an object $hist = new Math_Histogram(); // connect class to data series $hist->setData($series); // define number of bins and upper/lower limits $hist->setBinOptions(10,0,100); // calculate frequencies $hist->calculate(); // print as ASCII bar chart echo $hist->printHistogram(); >
Here, too, a number series is expressed as an array and passed to the setData() and calculate() methods for processing The number and size of the histogram bins can be controlled with the setBinOptions() method The printHistogram() method displays an ASCII representation of the histogram, as shown here:
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