Stochastics

Statistics

Mean (arithmetic mean), median, variance and standard deviation are determined for a prime notation. In addition, the distribution is presented as a histogram.

Formulas:

                    _
              Mean: x  = 1/n · Σ x(i)
                                         _                      _
          Variance: s2 = 1/(n-1)·Σ(x(i) -x)2  bzw.  1/n·Σ(x(i) -x)2
                          __
Standard Deviation: s =  √s2

The median is that value, which stands in the middle of the sorted list. In case of an even number of values the median ist the mean the two values in the middle of the list.

Example:

Dates:
1 2 3 4 5 4 3 4 5 4 3 2

Number of dates    n = 12

Maximum           max = 5

Minimum           min = 1

Mean               m = 3,3333333

Median             c = 3,5

Variance           v = 1,5151515

Standard deviation s = 1,2309149

+-------------------------+---------------+---------------+
|            x            |       H       |       h       |
+-------------------------+---------------+---------------+
|       1 <= x < 2        |       1       |   0,0833333   |
|       2 <= x < 3        |       2       |    0,166667   |
|       3 <= x < 4        |       3       |      0,25     |
|       4 <= x < 5        |       4       |    0,333333   |
+-------------------------+---------------+---------------+
eng.matheass.eu