Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 07 May 2009 17:49:09 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/08/t1241740192i0p6j1eapq3ho2w.htm/, Retrieved Mon, 29 Apr 2024 04:09:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39647, Retrieved Mon, 29 Apr 2024 04:09:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten(eige...] [2009-05-07 23:49:09] [f40d51a95968de218a79272805382c2a] [Current]
Feedback Forum

Post a new message
Dataseries X:
166,7
159,7
191
239,4
321,9
362,7
413,6
407,1
383,2
347,7
333,8
312,3
295,4
283,3
287,6
265,7
250,2
234,7
244
231,2
223,8
223,5
210,5
201,6
190,7
207,5
198,8
196,6
204,2
227,4
229,7
217,9
221,4
216,3
197
193,8
196,8
180,5
174,8
181,6
190
190,6
179
174,1
161,1
168,6
169,4
152,2
148,3
137,7
145
153,4
141,7
142,7
135,9
131,8
134,6
127,5
126,5
118,7
117,1
110,7
107,1
105,4
99
104
101,1
99,3
95,8
94,1
104,8
110,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39647&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39647&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean195.8847222222229.1248516312079321.4671679210954
Geometric Mean182.25799236839
Harmonic Mean170.046623143457
Quadratic Mean210.434055057108
Winsorized Mean ( 1 / 24 )195.8180555555569.0912226853954921.5392431064444
Winsorized Mean ( 2 / 24 )195.2430555555568.8696965741585822.0123714405729
Winsorized Mean ( 3 / 24 )194.4013888888898.6227542931695522.5451615898278
Winsorized Mean ( 4 / 24 )193.6680555555568.3847686882905823.0976026596912
Winsorized Mean ( 5 / 24 )192.9041666666678.1104825612759123.7845486022868
Winsorized Mean ( 6 / 24 )191.9791666666677.8633362931042624.4144672834382
Winsorized Mean ( 7 / 24 )191.1041666666677.6412664656035125.0094886138188
Winsorized Mean ( 8 / 24 )189.4152777777787.2064955755843226.2839650411385
Winsorized Mean ( 9 / 24 )188.8902777777786.9358016777328127.2340944211546
Winsorized Mean ( 10 / 24 )188.3208333333336.8128727052001627.6419128144859
Winsorized Mean ( 11 / 24 )186.5791666666676.1532072815218930.3222625421648
Winsorized Mean ( 12 / 24 )184.26255.6636399115870832.5342894104236
Winsorized Mean ( 13 / 24 )184.5513888888895.2581280671882535.0983061900918
Winsorized Mean ( 14 / 24 )183.8513888888895.0878176145816336.1356091778866
Winsorized Mean ( 15 / 24 )183.7680555555564.8011144158163338.2761250075957
Winsorized Mean ( 16 / 24 )183.61254.5920032968377839.9852718151231
Winsorized Mean ( 17 / 24 )183.5652777777784.4945555482581440.8416974285518
Winsorized Mean ( 18 / 24 )183.4402777777784.3450413608742842.2183041638221
Winsorized Mean ( 19 / 24 )183.5458333333334.0559139463431545.2538776121767
Winsorized Mean ( 20 / 24 )183.7402777777784.0040285170201345.8888534376675
Winsorized Mean ( 21 / 24 )183.7986111111113.8223712893046248.0849706111486
Winsorized Mean ( 22 / 24 )183.73753.5320361676286152.0202770526442
Winsorized Mean ( 23 / 24 )184.4722222222223.2881808203451556.1016052039555
Winsorized Mean ( 24 / 24 )182.9388888888892.9743468632183661.5055665333335
Trimmed Mean ( 1 / 24 )194.2285714285718.7250141677335822.2611181706567
Trimmed Mean ( 2 / 24 )192.5455882352948.2818667637898723.2490564901557
Trimmed Mean ( 3 / 24 )191.0742424242427.8927863293086524.2087184996657
Trimmed Mean ( 4 / 24 )189.82656257.5407725207211625.1733575012877
Trimmed Mean ( 5 / 24 )188.7112903225817.2062440258808326.1871912253921
Trimmed Mean ( 6 / 24 )187.7056.8912371381186227.2382151764473
Trimmed Mean ( 7 / 24 )186.8206896551726.5810755278733528.3875620123057
Trimmed Mean ( 8 / 24 )186.0339285714296.2620181992054329.7083021245505
Trimmed Mean ( 9 / 24 )185.4703703703705.986444989913330.9817213192260
Trimmed Mean ( 10 / 24 )184.9442307692315.7121608344525932.3772800047487
Trimmed Mean ( 11 / 24 )184.4585.3970249476646234.1777186114024
Trimmed Mean ( 12 / 24 )184.168755.1666347713354335.6457845678915
Trimmed Mean ( 13 / 24 )184.1565217391304.9915693679747236.8935114716938
Trimmed Mean ( 14 / 24 )184.1068181818184.8590061514015537.8898096535058
Trimmed Mean ( 15 / 24 )184.1380952380954.722760950085138.989501519186
Trimmed Mean ( 16 / 24 )184.18254.6071598229945739.9774496818486
Trimmed Mean ( 17 / 24 )184.254.4977626016779340.9648121337626
Trimmed Mean ( 18 / 24 )184.3305555555564.3679511368648342.2006908456082
Trimmed Mean ( 19 / 24 )184.4352941176474.2230352145587943.6736339497743
Trimmed Mean ( 20 / 24 )184.5406254.0948356031019745.0666749259005
Trimmed Mean ( 21 / 24 )184.6366666666673.9194166916857847.1082003243836
Trimmed Mean ( 22 / 24 )184.7392857142863.7164525501912649.7085011094191
Trimmed Mean ( 23 / 24 )184.8653846153853.5113045671535852.6486327459895
Trimmed Mean ( 24 / 24 )184.9166666666673.2855616656725856.2815997637995
Median190.3
Midrange253.85
Midmean - Weighted Average at Xnp183.021621621622
Midmean - Weighted Average at X(n+1)p184.330555555556
Midmean - Empirical Distribution Function183.021621621622
Midmean - Empirical Distribution Function - Averaging184.330555555556
Midmean - Empirical Distribution Function - Interpolation184.330555555556
Midmean - Closest Observation183.021621621622
Midmean - True Basic - Statistics Graphics Toolkit184.330555555556
Midmean - MS Excel (old versions)184.25
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 195.884722222222 & 9.12485163120793 & 21.4671679210954 \tabularnewline
Geometric Mean & 182.25799236839 &  &  \tabularnewline
Harmonic Mean & 170.046623143457 &  &  \tabularnewline
Quadratic Mean & 210.434055057108 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 195.818055555556 & 9.09122268539549 & 21.5392431064444 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 195.243055555556 & 8.86969657415858 & 22.0123714405729 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 194.401388888889 & 8.62275429316955 & 22.5451615898278 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 193.668055555556 & 8.38476868829058 & 23.0976026596912 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 192.904166666667 & 8.11048256127591 & 23.7845486022868 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 191.979166666667 & 7.86333629310426 & 24.4144672834382 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 191.104166666667 & 7.64126646560351 & 25.0094886138188 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 189.415277777778 & 7.20649557558432 & 26.2839650411385 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 188.890277777778 & 6.93580167773281 & 27.2340944211546 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 188.320833333333 & 6.81287270520016 & 27.6419128144859 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 186.579166666667 & 6.15320728152189 & 30.3222625421648 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 184.2625 & 5.66363991158708 & 32.5342894104236 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 184.551388888889 & 5.25812806718825 & 35.0983061900918 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 183.851388888889 & 5.08781761458163 & 36.1356091778866 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 183.768055555556 & 4.80111441581633 & 38.2761250075957 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 183.6125 & 4.59200329683778 & 39.9852718151231 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 183.565277777778 & 4.49455554825814 & 40.8416974285518 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 183.440277777778 & 4.34504136087428 & 42.2183041638221 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 183.545833333333 & 4.05591394634315 & 45.2538776121767 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 183.740277777778 & 4.00402851702013 & 45.8888534376675 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 183.798611111111 & 3.82237128930462 & 48.0849706111486 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 183.7375 & 3.53203616762861 & 52.0202770526442 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 184.472222222222 & 3.28818082034515 & 56.1016052039555 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 182.938888888889 & 2.97434686321836 & 61.5055665333335 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 194.228571428571 & 8.72501416773358 & 22.2611181706567 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 192.545588235294 & 8.28186676378987 & 23.2490564901557 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 191.074242424242 & 7.89278632930865 & 24.2087184996657 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 189.8265625 & 7.54077252072116 & 25.1733575012877 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 188.711290322581 & 7.20624402588083 & 26.1871912253921 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 187.705 & 6.89123713811862 & 27.2382151764473 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 186.820689655172 & 6.58107552787335 & 28.3875620123057 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 186.033928571429 & 6.26201819920543 & 29.7083021245505 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 185.470370370370 & 5.9864449899133 & 30.9817213192260 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 184.944230769231 & 5.71216083445259 & 32.3772800047487 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 184.458 & 5.39702494766462 & 34.1777186114024 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 184.16875 & 5.16663477133543 & 35.6457845678915 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 184.156521739130 & 4.99156936797472 & 36.8935114716938 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 184.106818181818 & 4.85900615140155 & 37.8898096535058 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 184.138095238095 & 4.7227609500851 & 38.989501519186 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 184.1825 & 4.60715982299457 & 39.9774496818486 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 184.25 & 4.49776260167793 & 40.9648121337626 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 184.330555555556 & 4.36795113686483 & 42.2006908456082 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 184.435294117647 & 4.22303521455879 & 43.6736339497743 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 184.540625 & 4.09483560310197 & 45.0666749259005 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 184.636666666667 & 3.91941669168578 & 47.1082003243836 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 184.739285714286 & 3.71645255019126 & 49.7085011094191 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 184.865384615385 & 3.51130456715358 & 52.6486327459895 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 184.916666666667 & 3.28556166567258 & 56.2815997637995 \tabularnewline
Median & 190.3 &  &  \tabularnewline
Midrange & 253.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 183.021621621622 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 184.330555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 183.021621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 184.330555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 184.330555555556 &  &  \tabularnewline
Midmean - Closest Observation & 183.021621621622 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 184.330555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 184.25 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39647&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]195.884722222222[/C][C]9.12485163120793[/C][C]21.4671679210954[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]182.25799236839[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]170.046623143457[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]210.434055057108[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]195.818055555556[/C][C]9.09122268539549[/C][C]21.5392431064444[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]195.243055555556[/C][C]8.86969657415858[/C][C]22.0123714405729[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]194.401388888889[/C][C]8.62275429316955[/C][C]22.5451615898278[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]193.668055555556[/C][C]8.38476868829058[/C][C]23.0976026596912[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]192.904166666667[/C][C]8.11048256127591[/C][C]23.7845486022868[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]191.979166666667[/C][C]7.86333629310426[/C][C]24.4144672834382[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]191.104166666667[/C][C]7.64126646560351[/C][C]25.0094886138188[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]189.415277777778[/C][C]7.20649557558432[/C][C]26.2839650411385[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]188.890277777778[/C][C]6.93580167773281[/C][C]27.2340944211546[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]188.320833333333[/C][C]6.81287270520016[/C][C]27.6419128144859[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]186.579166666667[/C][C]6.15320728152189[/C][C]30.3222625421648[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]184.2625[/C][C]5.66363991158708[/C][C]32.5342894104236[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]184.551388888889[/C][C]5.25812806718825[/C][C]35.0983061900918[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]183.851388888889[/C][C]5.08781761458163[/C][C]36.1356091778866[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]183.768055555556[/C][C]4.80111441581633[/C][C]38.2761250075957[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]183.6125[/C][C]4.59200329683778[/C][C]39.9852718151231[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]183.565277777778[/C][C]4.49455554825814[/C][C]40.8416974285518[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]183.440277777778[/C][C]4.34504136087428[/C][C]42.2183041638221[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]183.545833333333[/C][C]4.05591394634315[/C][C]45.2538776121767[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]183.740277777778[/C][C]4.00402851702013[/C][C]45.8888534376675[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]183.798611111111[/C][C]3.82237128930462[/C][C]48.0849706111486[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]183.7375[/C][C]3.53203616762861[/C][C]52.0202770526442[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]184.472222222222[/C][C]3.28818082034515[/C][C]56.1016052039555[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]182.938888888889[/C][C]2.97434686321836[/C][C]61.5055665333335[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]194.228571428571[/C][C]8.72501416773358[/C][C]22.2611181706567[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]192.545588235294[/C][C]8.28186676378987[/C][C]23.2490564901557[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]191.074242424242[/C][C]7.89278632930865[/C][C]24.2087184996657[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]189.8265625[/C][C]7.54077252072116[/C][C]25.1733575012877[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]188.711290322581[/C][C]7.20624402588083[/C][C]26.1871912253921[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]187.705[/C][C]6.89123713811862[/C][C]27.2382151764473[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]186.820689655172[/C][C]6.58107552787335[/C][C]28.3875620123057[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]186.033928571429[/C][C]6.26201819920543[/C][C]29.7083021245505[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]185.470370370370[/C][C]5.9864449899133[/C][C]30.9817213192260[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]184.944230769231[/C][C]5.71216083445259[/C][C]32.3772800047487[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]184.458[/C][C]5.39702494766462[/C][C]34.1777186114024[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]184.16875[/C][C]5.16663477133543[/C][C]35.6457845678915[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]184.156521739130[/C][C]4.99156936797472[/C][C]36.8935114716938[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]184.106818181818[/C][C]4.85900615140155[/C][C]37.8898096535058[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]184.138095238095[/C][C]4.7227609500851[/C][C]38.989501519186[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]184.1825[/C][C]4.60715982299457[/C][C]39.9774496818486[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]184.25[/C][C]4.49776260167793[/C][C]40.9648121337626[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]184.330555555556[/C][C]4.36795113686483[/C][C]42.2006908456082[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]184.435294117647[/C][C]4.22303521455879[/C][C]43.6736339497743[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]184.540625[/C][C]4.09483560310197[/C][C]45.0666749259005[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]184.636666666667[/C][C]3.91941669168578[/C][C]47.1082003243836[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]184.739285714286[/C][C]3.71645255019126[/C][C]49.7085011094191[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]184.865384615385[/C][C]3.51130456715358[/C][C]52.6486327459895[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]184.916666666667[/C][C]3.28556166567258[/C][C]56.2815997637995[/C][/ROW]
[ROW][C]Median[/C][C]190.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]253.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]184.330555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]184.330555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]184.330555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]184.330555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]184.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39647&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean195.8847222222229.1248516312079321.4671679210954
Geometric Mean182.25799236839
Harmonic Mean170.046623143457
Quadratic Mean210.434055057108
Winsorized Mean ( 1 / 24 )195.8180555555569.0912226853954921.5392431064444
Winsorized Mean ( 2 / 24 )195.2430555555568.8696965741585822.0123714405729
Winsorized Mean ( 3 / 24 )194.4013888888898.6227542931695522.5451615898278
Winsorized Mean ( 4 / 24 )193.6680555555568.3847686882905823.0976026596912
Winsorized Mean ( 5 / 24 )192.9041666666678.1104825612759123.7845486022868
Winsorized Mean ( 6 / 24 )191.9791666666677.8633362931042624.4144672834382
Winsorized Mean ( 7 / 24 )191.1041666666677.6412664656035125.0094886138188
Winsorized Mean ( 8 / 24 )189.4152777777787.2064955755843226.2839650411385
Winsorized Mean ( 9 / 24 )188.8902777777786.9358016777328127.2340944211546
Winsorized Mean ( 10 / 24 )188.3208333333336.8128727052001627.6419128144859
Winsorized Mean ( 11 / 24 )186.5791666666676.1532072815218930.3222625421648
Winsorized Mean ( 12 / 24 )184.26255.6636399115870832.5342894104236
Winsorized Mean ( 13 / 24 )184.5513888888895.2581280671882535.0983061900918
Winsorized Mean ( 14 / 24 )183.8513888888895.0878176145816336.1356091778866
Winsorized Mean ( 15 / 24 )183.7680555555564.8011144158163338.2761250075957
Winsorized Mean ( 16 / 24 )183.61254.5920032968377839.9852718151231
Winsorized Mean ( 17 / 24 )183.5652777777784.4945555482581440.8416974285518
Winsorized Mean ( 18 / 24 )183.4402777777784.3450413608742842.2183041638221
Winsorized Mean ( 19 / 24 )183.5458333333334.0559139463431545.2538776121767
Winsorized Mean ( 20 / 24 )183.7402777777784.0040285170201345.8888534376675
Winsorized Mean ( 21 / 24 )183.7986111111113.8223712893046248.0849706111486
Winsorized Mean ( 22 / 24 )183.73753.5320361676286152.0202770526442
Winsorized Mean ( 23 / 24 )184.4722222222223.2881808203451556.1016052039555
Winsorized Mean ( 24 / 24 )182.9388888888892.9743468632183661.5055665333335
Trimmed Mean ( 1 / 24 )194.2285714285718.7250141677335822.2611181706567
Trimmed Mean ( 2 / 24 )192.5455882352948.2818667637898723.2490564901557
Trimmed Mean ( 3 / 24 )191.0742424242427.8927863293086524.2087184996657
Trimmed Mean ( 4 / 24 )189.82656257.5407725207211625.1733575012877
Trimmed Mean ( 5 / 24 )188.7112903225817.2062440258808326.1871912253921
Trimmed Mean ( 6 / 24 )187.7056.8912371381186227.2382151764473
Trimmed Mean ( 7 / 24 )186.8206896551726.5810755278733528.3875620123057
Trimmed Mean ( 8 / 24 )186.0339285714296.2620181992054329.7083021245505
Trimmed Mean ( 9 / 24 )185.4703703703705.986444989913330.9817213192260
Trimmed Mean ( 10 / 24 )184.9442307692315.7121608344525932.3772800047487
Trimmed Mean ( 11 / 24 )184.4585.3970249476646234.1777186114024
Trimmed Mean ( 12 / 24 )184.168755.1666347713354335.6457845678915
Trimmed Mean ( 13 / 24 )184.1565217391304.9915693679747236.8935114716938
Trimmed Mean ( 14 / 24 )184.1068181818184.8590061514015537.8898096535058
Trimmed Mean ( 15 / 24 )184.1380952380954.722760950085138.989501519186
Trimmed Mean ( 16 / 24 )184.18254.6071598229945739.9774496818486
Trimmed Mean ( 17 / 24 )184.254.4977626016779340.9648121337626
Trimmed Mean ( 18 / 24 )184.3305555555564.3679511368648342.2006908456082
Trimmed Mean ( 19 / 24 )184.4352941176474.2230352145587943.6736339497743
Trimmed Mean ( 20 / 24 )184.5406254.0948356031019745.0666749259005
Trimmed Mean ( 21 / 24 )184.6366666666673.9194166916857847.1082003243836
Trimmed Mean ( 22 / 24 )184.7392857142863.7164525501912649.7085011094191
Trimmed Mean ( 23 / 24 )184.8653846153853.5113045671535852.6486327459895
Trimmed Mean ( 24 / 24 )184.9166666666673.2855616656725856.2815997637995
Median190.3
Midrange253.85
Midmean - Weighted Average at Xnp183.021621621622
Midmean - Weighted Average at X(n+1)p184.330555555556
Midmean - Empirical Distribution Function183.021621621622
Midmean - Empirical Distribution Function - Averaging184.330555555556
Midmean - Empirical Distribution Function - Interpolation184.330555555556
Midmean - Closest Observation183.021621621622
Midmean - True Basic - Statistics Graphics Toolkit184.330555555556
Midmean - MS Excel (old versions)184.25
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')