g01ae:: Simple Calculations on Statistical Data (NAG Toolbox)

If the boundary values of the classes are to be function-calculated, then they are determined in one of the following ways:

(a)	if $k > 2$ , the range of $x$ values is divided into $k - 2$ intervals of equal length, and two extreme intervals, defined by the class boundary values $y_{1}, y_{2}, \dots, y_{k - 1}$ ;
(b)	if $k = 2$ , $y_{1} = \frac{1}{2} (a + b)$ .

However formed, the values

y_{1}, \dots, y_{k - 1}

are assumed to be in ascending order. The class frequencies are formed with

$f_{1} =$ the number of $x$ values in the interval $(- \infty, y_{1})$
$f_{i} =$ the number of $x$ values in the interval $[y_{i - 1}, y_{i})$ , $i = 2, \dots, k - 1$
$f_{k} =$ the number of $x$ values in the interval $[y_{k - 1}, \infty)$ ,

where [ means inclusive, and ) means exclusive. If the class boundary values are function-calculated and

k > 2

, then

f_{1} = f_{k} = 0

, and

y_{1}

and

y_{k - 1}

are chosen so that

y_{1} < a

and

y_{k - 1} > b

If a frequency distribution is required for a discrete variable, then it is suggested that you supply the class boundary values; function-calculated boundary values may be slightly imprecise (due to the adjustment of

y_{1}

and

y_{k - 1}

outlined above) and cause values very close to a class boundary to be assigned to the wrong class.

References

Parameters

Compulsory Input Parameters

Optional Input Parameters

Output Parameters

Error Indicators and Warnings

Accuracy

Further Comments

Example

This example summarises a number of datasets. For each dataset the sample observations and optionally class boundary values are read. nag_stat_frequency_table (g01ae) is then called and the frequency distribution and largest and smallest observations printed.

function g01ae_example


fprintf('g01ae example results\n\n');

x = [22.3; 21.6; 22.6; 22.4; 22.4; 22.4; 22.1; 21.9; 23.1; 23.4; 23.4;
     22.6; 22.5; 22.5; 22.1; 22.6; 22.3; 22.4; 21.8; 22.3; 22.1; 23.6;
     20.8; 22.2; 23.1; 21.1; 21.7; 21.4; 21.6; 22.5; 21.2; 22.6; 22.2;
     22.2; 21.4; 21.7; 23.2; 23.1; 22.3; 22.3; 21.1; 21.4; 21.5; 21.8;
     22.8; 21.4; 20.7; 21.6; 23.2; 23.6; 22.7; 21.7; 23.0; 21.9; 22.6;
     22.1; 22.2; 23.4; 21.5; 23.0; 22.8; 21.4; 23.2; 21.8; 21.2; 22.0;
     22.4; 22.8; 23.2; 23.6];

k = int64(7);
[cb, ifreq, xmin, xmax, ifail] = g01ae(k, x);
 
fprintf('Number of cases     %3d\n',size(x,1));
fprintf('Number of classes   %3d\n\n',k);
fprintf('Routine-supplied class boundaries\n\n');
fprintf('        Class            Frequency\n');
fprintf('%9s to%7.2f%14d\n', 'Up', cb(1), ifreq(1));
for i=2:k-1
  fprintf('%7.2f   to%7.2f%14d\n', cb(i-1), cb(i), ifreq(i));
end
fprintf('%7.2f  and%7s%14d\n\n', cb(k-1), 'over', ifreq(k));
fprintf('Total frequency = %5d\n',sum(ifreq));
fprintf('Minimum         = %8.2f\n',xmin);
fprintf('Maximum         = %8.2f\n',xmax);

g01ae example results

Number of cases      70
Number of classes     7

Routine-supplied class boundaries

        Class            Frequency
       Up to  20.70             0
  20.70   to  21.28             6
  21.28   to  21.86            16
  21.86   to  22.44            21
  22.44   to  23.02            14
  23.02   to  23.60            13
  23.60  and   over             0

Total frequency =    70
Minimum         =    20.70
Maximum         =    23.60

NAG Toolbox: nag_stat_frequency_table (g01ae)

▸▿ Contents

Purpose

Syntax

Description