Descriptive Statistics - Frequency Table - Examples

Data

Airline Data (°)

Download

ASCII Text or MS Excel 2000 Sheet.

Output

+---------------------------------------------+
¦ FRTUND : FREQUENCY TABLE 1 - UNGROUPED DATA ¦
+---------------------------------------------+

     INTERVALS         NON-CUMUL.      CUMULATIVE
  Lower     Upper    Abs.    Rel.    Abs.    Rel.
  -----------------------------------------------
   1.00      1.50      24    .169      24    .169
   1.50      2.00      24    .169      48    .338
   2.00      2.50      21    .148      69    .486
   2.50      3.00      13    .092      82    .577
   3.00      3.50      21    .148     103    .725
   3.50      4.00      13    .092     116    .817
   4.00      4.50      13    .092     129    .908
   4.50      5.00       8    .056     137    .965
   5.00      5.50       4    .028     141    .993
   5.50      6.00       1    .007     142   1.000

+---------------------------------------------+
¦ FRTUND : FREQUENCY TABLE 2 - UNGROUPED DATA ¦
+---------------------------------------------+

     INTERVALS
  Lower     Upper     CENTER       MEAN     MEDIAN
  ------------------------------------------------
   1.00      1.50      1.250      1.308      1.165
   1.50      2.00      1.750      1.802      1.685
   2.00      2.50      2.250      2.269      2.010
   2.50      3.00      2.750      2.725      2.690
   3.00      3.50      3.250      3.230      3.010
   3.50      4.00      3.750      3.682      3.630
   4.00      4.50      4.250      4.145      4.060
   4.50      5.00      4.750      4.690      4.675
   5.00      5.50      5.250      5.240      5.415
   5.50      6.00      5.750      5.590      5.590

+---------------------------------------------+
¦ FRTUND : FREQUENCY TABLE 3 - UNGROUPED DATA ¦
+---------------------------------------------+

                                     GROUPED                       UNGROUPED
                    ------------------------------------------
                            CENTER          MEAN        MEDIAN
                    ------------------------------------------

Mean              :         2.7606        2.7560        2.6296        2.7560

Var. Biased       :         1.3855        1.2732        1.3868        1.2902
     Unbiased     :         1.3953        1.2822        1.3966        1.2993

St. Dev. Biased   :         1.1771        1.1283        1.1776        1.1359
         Unbiased :         1.1812        1.1323        1.1818        1.1399

Observations Tot. :       144           144           144           144
Observations Used :       142           142           142           142
Intervals         :        10            10            10
Frequencies       :       142           142           142

+---------------------------------------------+
¦ FRTUND : FREQUENCY TABLE 4 - UNGROUPED DATA ¦
+---------------------------------------------+

                                     GROUPED                       UNGROUPED
                    ------------------------------------------
                            CENTER          MEAN        MEDIAN
                    ------------------------------------------
MOMENT NOT CENTERED

Order 1           :    2.76056e+00   2.75599e+00   2.62965e+00   2.75599e+00
Order 2           :    9.00616e+00   8.86863e+00   8.30181e+00   8.88565e+00
Order 3           :    3.32095e+01   3.21159e+01   3.00567e+01   3.22578e+01
Order 4           :    1.33273e+02   1.26572e+02   1.19798e+02   1.27490e+02

MOMENT CENTERED

Order 1           :    1.87643e-16   6.50497e-16   4.97255e-16  -1.82014e-15
Order 2           :    1.38545e+00   1.27317e+00   1.38676e+00   1.29019e+00
Order 3           :    6.98171e-01   6.56435e-01   9.32496e-01   6.57601e-01
Order 4           :    4.13991e+00   3.62268e+00   4.63448e+00   3.75245e+00

+---------------------------------------------+
¦ FRTUND : FREQUENCY TABLE 5 - UNGROUPED DATA ¦
+---------------------------------------------+

                                     GROUPED                       UNGROUPED
                    ------------------------------------------
                            CENTER          MEAN        MEDIAN
                    ------------------------------------------
SKEWNESS

3rd Cent. Moment  :    6.98171e-01   6.56435e-01   9.32496e-01   6.57601e-01
beta  1           :          .1833         .2088         .3261         .2014
gamma 1           :          .4281         .4569         .5710         .4487

KURTOSIS

4th Cent. Moment  :    4.13991e+00   3.62268e+00   4.63448e+00   3.75245e+00
beta  2           :         2.1568        2.2349        2.4099        2.2543
gamma 2           :         -.8432        -.7651        -.5901        -.7457

(°) Box, G.E. and Jenkins, G.M.

Time Series Analysis : Forecasting and Control

Holden Day, San Francisco, 1976, p. 531.