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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 08 Dec 2007 05:35:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/08/t11971165033qa7bvj0roewtmm.htm/, Retrieved Sun, 28 Apr 2024 22:06:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2913, Retrieved Sun, 28 Apr 2024 22:06:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact262
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2007-12-08 12:35:27] [8e05505c645e933583b5ad9ab4281af9] [Current]
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Dataseries X:
153,4
159,5
157,4
169,1
172,6
161,7
159,2
157,4
153,9
144,8
142,2
140,1
143,4
153,3
166,9
170,6
182,8
170,3
156,6
155,2
154,7
151,6
152,1
153,2
149,5
149,7
144,3
140
137,8
132,2
128,9
123,1
120,4
122,8
126
124,5
120,6
114,7
111,7
109,1
108
107,7
99,9
103,7
103,4
103,4
104,7
105,8
105,3
103
103,8
103,4
105,8
101,4
97
94,3
96,6
97,1
95,7
96,9
97,4
95,3
93,6
91,5
93,1
91,7
94,3
93,9
90,9
88,3
91,3
91,7
92,4
92
95,6
95,8
96,4
99
107
109,7
116,2
115,9
113,8
112,6
113,7
115,9
110,3
111,3
113,4
108,2
104,8
106
110,9
115
118,4
121,4
128,8
131,7
141,7
142,9
139,4
134,7
125
113,6
111,5
108,5
112,3
116,6
115,5
120,1
132,9
128,1
129,3
132,5
131
124,9
120,8
122
122,1
127,4
135,2
137,3
135
136
138,4
134,7
138,4
133,9
133,6
141,2
151,8
155,4
156,6
161,6
160,7
156
159,5
168,7
169,9
169,9
185,9




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2913&T=0

[TABLE]
[ROW][C]Summary of compuational 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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2913&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean125.9283687943262.0518665548487661.3725919440254
Geometric Mean123.637560644502
Harmonic Mean121.419074567177
Quadratic Mean128.247323392915
Winsorized Mean ( 1 / 47 )125.9248226950352.0450518917989261.5753679405497
Winsorized Mean ( 2 / 47 )125.7858156028372.0179851371451962.3323796035406
Winsorized Mean ( 3 / 47 )125.7475177304962.0105503341020262.5438297154892
Winsorized Mean ( 4 / 47 )125.7446808510642.0085093611006962.6059720140683
Winsorized Mean ( 5 / 47 )125.7304964539012.0062702983125262.6687722784179
Winsorized Mean ( 6 / 47 )125.7432624113482.0047295408306262.7233049896836
Winsorized Mean ( 7 / 47 )125.7234042553191.9961451295471162.9830979693562
Winsorized Mean ( 8 / 47 )125.7404255319151.9879352361849963.251771608627
Winsorized Mean ( 9 / 47 )125.6574468085111.9667322385414163.8914867748862
Winsorized Mean ( 10 / 47 )125.3099290780141.9115142776877265.5553194348078
Winsorized Mean ( 11 / 47 )125.3333333333331.9068087533230565.7293675178023
Winsorized Mean ( 12 / 47 )125.2567375886521.8964931389017166.046501840334
Winsorized Mean ( 13 / 47 )125.2382978723401.8712287733365466.9283733004121
Winsorized Mean ( 14 / 47 )125.2680851063831.867836961037667.0658562387563
Winsorized Mean ( 15 / 47 )125.2468085106381.8624638476439367.2479139227744
Winsorized Mean ( 16 / 47 )125.0539007092201.8350142016601268.1487372664936
Winsorized Mean ( 17 / 47 )125.1262411347521.826832717159568.4935407382607
Winsorized Mean ( 18 / 47 )125.0496453900711.8111686667245369.0436223238234
Winsorized Mean ( 19 / 47 )125.0900709219861.8066480028060569.2387619102881
Winsorized Mean ( 20 / 47 )125.0191489361701.7945176882461269.6672703507083
Winsorized Mean ( 21 / 47 )124.9446808510641.7818911852526170.1191418898852
Winsorized Mean ( 22 / 47 )124.9602836879431.7728742081391870.4845742096402
Winsorized Mean ( 23 / 47 )125.1397163120571.7343977752490672.1516817525247
Winsorized Mean ( 24 / 47 )125.1567375886521.7015251234284273.5556212866684
Winsorized Mean ( 25 / 47 )125.3340425531911.6630594692203275.3635362251665
Winsorized Mean ( 26 / 47 )125.6106382978721.6310533583792177.0119736749094
Winsorized Mean ( 27 / 47 )125.6680851063831.6211811394407377.5163749744432
Winsorized Mean ( 28 / 47 )125.4496453900711.5948945343176278.657016304683
Winsorized Mean ( 29 / 47 )125.3879432624111.5875460328637178.9822409346009
Winsorized Mean ( 30 / 47 )125.4092198581561.5761950969009779.5645285946702
Winsorized Mean ( 31 / 47 )125.0134751773051.5250715331465481.9722042279395
Winsorized Mean ( 32 / 47 )125.1723404255321.4997112543373183.4642935855293
Winsorized Mean ( 33 / 47 )124.0957446808511.3742865413777490.2983045707802
Winsorized Mean ( 34 / 47 )124.0957446808511.3493068776191491.9699934382749
Winsorized Mean ( 35 / 47 )123.9964539007091.3132519214788994.4193965169098
Winsorized Mean ( 36 / 47 )123.8687943262411.2998398836598195.295425139193
Winsorized Mean ( 37 / 47 )123.7375886524821.2755262096311597.0090521999259
Winsorized Mean ( 38 / 47 )123.8723404255321.23507589583520100.295326662306
Winsorized Mean ( 39 / 47 )123.9276595744681.20206598007298103.095555176550
Winsorized Mean ( 40 / 47 )123.7007092198581.16211014813880106.444909217920
Winsorized Mean ( 41 / 47 )123.7297872340431.15357764483166107.257441914192
Winsorized Mean ( 42 / 47 )123.6404255319151.12706502075817109.701235735932
Winsorized Mean ( 43 / 47 )123.5184397163121.07930359683488114.442720360181
Winsorized Mean ( 44 / 47 )123.7056737588651.06154709843616116.533382212721
Winsorized Mean ( 45 / 47 )123.7056737588651.02470139127766120.723632086243
Winsorized Mean ( 46 / 47 )123.7382978723400.990502855299827124.924726072480
Winsorized Mean ( 47 / 47 )123.4382978723400.936189359203676131.851848836797
Trimmed Mean ( 1 / 47 )125.7676258992812.0177039943065862.3320498220566
Trimmed Mean ( 2 / 47 )125.6058394160581.9877843903037163.188864963804
Trimmed Mean ( 3 / 47 )125.5118518518521.9703978580525563.6987354299613
Trimmed Mean ( 4 / 47 )125.4285714285711.9541796614613764.1847696515139
Trimmed Mean ( 5 / 47 )125.3435114503821.9369261805888964.7125908599537
Trimmed Mean ( 6 / 47 )125.2589147286821.9184732845951565.2909351068264
Trimmed Mean ( 7 / 47 )125.1692913385831.8984510463050965.932324977353
Trimmed Mean ( 8 / 47 )125.081.878028135417466.6017711029662
Trimmed Mean ( 9 / 47 )124.9853658536591.8568993009576267.3086396172387
Trimmed Mean ( 10 / 47 )124.8983471074381.8370052072606867.9901976400409
Trimmed Mean ( 11 / 47 )124.8495798319331.8233377153915268.473096770844
Trimmed Mean ( 12 / 47 )124.7965811965811.8086978883487768.9980244907083
Trimmed Mean ( 13 / 47 )124.7495652173911.7937072705879169.5484526728281
Trimmed Mean ( 14 / 47 )124.7026548672571.7801229290430370.052833336794
Trimmed Mean ( 15 / 47 )124.6513513513511.7652273577860470.6148988692823
Trimmed Mean ( 16 / 47 )124.61.7490985980037271.2366930842027
Trimmed Mean ( 17 / 47 )124.562616822431.7341668681071771.8285068831865
Trimmed Mean ( 18 / 47 )124.5180952380951.7181842473877572.4707466195242
Trimmed Mean ( 19 / 47 )124.4776699029131.7018572692597173.1422500296158
Trimmed Mean ( 20 / 47 )124.4326732673271.6838235067262173.8988811893096
Trimmed Mean ( 21 / 47 )124.3909090909091.6647150545857874.7220425190789
Trimmed Mean ( 22 / 47 )124.3525773195881.6444096518378175.6214105047423
Trimmed Mean ( 23 / 47 )124.3115789473681.6222921193171276.6271237264567
Trimmed Mean ( 24 / 47 )124.2569892473121.6012591453331477.5995500849806
Trimmed Mean ( 25 / 47 )124.1989010989011.5807746779446578.5683771582089
Trimmed Mean ( 26 / 47 )124.1269662921351.5613359926136479.5004834829623
Trimmed Mean ( 27 / 47 )124.0344827586211.5421744817021880.4283070627114
Trimmed Mean ( 28 / 47 )123.9341176470591.5209641945383681.4839153295618
Trimmed Mean ( 29 / 47 )123.8421686746991.4994132660705082.5937528212293
Trimmed Mean ( 30 / 47 )123.7493827160491.4751701340012883.8882104943307
Trimmed Mean ( 31 / 47 )123.6506329113921.4481685188987085.3841464565368
Trimmed Mean ( 32 / 47 )123.5701298701301.4229938030133686.8381363351372
Trimmed Mean ( 33 / 47 )123.4761.3963063759417288.4304491675213
Trimmed Mean ( 34 / 47 )123.4397260273971.3805202454583489.4153681798523
Trimmed Mean ( 35 / 47 )123.4014084507041.3644501888077290.4403909083225
Trimmed Mean ( 36 / 47 )123.3666666666671.349349669172591.426758745435
Trimmed Mean ( 37 / 47 )123.3373134328361.3326041128135392.5536040650762
Trimmed Mean ( 38 / 47 )123.3138461538461.3152505554717193.7569238354134
Trimmed Mean ( 39 / 47 )123.2809523809521.2991053228081194.896811071847
Trimmed Mean ( 40 / 47 )123.2426229508201.2833644713057296.0308826575436
Trimmed Mean ( 41 / 47 )123.2152542372881.2691037292610697.0884029385295
Trimmed Mean ( 42 / 47 )123.1842105263161.2521054685894998.3816568304618
Trimmed Mean ( 43 / 47 )123.1563636363641.2344242067176199.7682668293116
Trimmed Mean ( 44 / 47 )123.1339622641511.21906107066954101.007213852316
Trimmed Mean ( 45 / 47 )123.0980392156861.20165405675931102.440497348850
Trimmed Mean ( 46 / 47 )123.0591836734691.18488897829240103.857142675777
Trimmed Mean ( 47 / 47 )123.0148936170211.16838154592122105.286577014557
Median122.1
Midrange137.1
Midmean - Weighted Average at Xnp123.115714285714
Midmean - Weighted Average at X(n+1)p123.401408450704
Midmean - Empirical Distribution Function123.401408450704
Midmean - Empirical Distribution Function - Averaging123.401408450704
Midmean - Empirical Distribution Function - Interpolation123.401408450704
Midmean - Closest Observation123.15
Midmean - True Basic - Statistics Graphics Toolkit123.401408450704
Midmean - MS Excel (old versions)123.401408450704
Number of observations141

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 125.928368794326 & 2.05186655484876 & 61.3725919440254 \tabularnewline
Geometric Mean & 123.637560644502 &  &  \tabularnewline
Harmonic Mean & 121.419074567177 &  &  \tabularnewline
Quadratic Mean & 128.247323392915 &  &  \tabularnewline
Winsorized Mean ( 1 / 47 ) & 125.924822695035 & 2.04505189179892 & 61.5753679405497 \tabularnewline
Winsorized Mean ( 2 / 47 ) & 125.785815602837 & 2.01798513714519 & 62.3323796035406 \tabularnewline
Winsorized Mean ( 3 / 47 ) & 125.747517730496 & 2.01055033410202 & 62.5438297154892 \tabularnewline
Winsorized Mean ( 4 / 47 ) & 125.744680851064 & 2.00850936110069 & 62.6059720140683 \tabularnewline
Winsorized Mean ( 5 / 47 ) & 125.730496453901 & 2.00627029831252 & 62.6687722784179 \tabularnewline
Winsorized Mean ( 6 / 47 ) & 125.743262411348 & 2.00472954083062 & 62.7233049896836 \tabularnewline
Winsorized Mean ( 7 / 47 ) & 125.723404255319 & 1.99614512954711 & 62.9830979693562 \tabularnewline
Winsorized Mean ( 8 / 47 ) & 125.740425531915 & 1.98793523618499 & 63.251771608627 \tabularnewline
Winsorized Mean ( 9 / 47 ) & 125.657446808511 & 1.96673223854141 & 63.8914867748862 \tabularnewline
Winsorized Mean ( 10 / 47 ) & 125.309929078014 & 1.91151427768772 & 65.5553194348078 \tabularnewline
Winsorized Mean ( 11 / 47 ) & 125.333333333333 & 1.90680875332305 & 65.7293675178023 \tabularnewline
Winsorized Mean ( 12 / 47 ) & 125.256737588652 & 1.89649313890171 & 66.046501840334 \tabularnewline
Winsorized Mean ( 13 / 47 ) & 125.238297872340 & 1.87122877333654 & 66.9283733004121 \tabularnewline
Winsorized Mean ( 14 / 47 ) & 125.268085106383 & 1.8678369610376 & 67.0658562387563 \tabularnewline
Winsorized Mean ( 15 / 47 ) & 125.246808510638 & 1.86246384764393 & 67.2479139227744 \tabularnewline
Winsorized Mean ( 16 / 47 ) & 125.053900709220 & 1.83501420166012 & 68.1487372664936 \tabularnewline
Winsorized Mean ( 17 / 47 ) & 125.126241134752 & 1.8268327171595 & 68.4935407382607 \tabularnewline
Winsorized Mean ( 18 / 47 ) & 125.049645390071 & 1.81116866672453 & 69.0436223238234 \tabularnewline
Winsorized Mean ( 19 / 47 ) & 125.090070921986 & 1.80664800280605 & 69.2387619102881 \tabularnewline
Winsorized Mean ( 20 / 47 ) & 125.019148936170 & 1.79451768824612 & 69.6672703507083 \tabularnewline
Winsorized Mean ( 21 / 47 ) & 124.944680851064 & 1.78189118525261 & 70.1191418898852 \tabularnewline
Winsorized Mean ( 22 / 47 ) & 124.960283687943 & 1.77287420813918 & 70.4845742096402 \tabularnewline
Winsorized Mean ( 23 / 47 ) & 125.139716312057 & 1.73439777524906 & 72.1516817525247 \tabularnewline
Winsorized Mean ( 24 / 47 ) & 125.156737588652 & 1.70152512342842 & 73.5556212866684 \tabularnewline
Winsorized Mean ( 25 / 47 ) & 125.334042553191 & 1.66305946922032 & 75.3635362251665 \tabularnewline
Winsorized Mean ( 26 / 47 ) & 125.610638297872 & 1.63105335837921 & 77.0119736749094 \tabularnewline
Winsorized Mean ( 27 / 47 ) & 125.668085106383 & 1.62118113944073 & 77.5163749744432 \tabularnewline
Winsorized Mean ( 28 / 47 ) & 125.449645390071 & 1.59489453431762 & 78.657016304683 \tabularnewline
Winsorized Mean ( 29 / 47 ) & 125.387943262411 & 1.58754603286371 & 78.9822409346009 \tabularnewline
Winsorized Mean ( 30 / 47 ) & 125.409219858156 & 1.57619509690097 & 79.5645285946702 \tabularnewline
Winsorized Mean ( 31 / 47 ) & 125.013475177305 & 1.52507153314654 & 81.9722042279395 \tabularnewline
Winsorized Mean ( 32 / 47 ) & 125.172340425532 & 1.49971125433731 & 83.4642935855293 \tabularnewline
Winsorized Mean ( 33 / 47 ) & 124.095744680851 & 1.37428654137774 & 90.2983045707802 \tabularnewline
Winsorized Mean ( 34 / 47 ) & 124.095744680851 & 1.34930687761914 & 91.9699934382749 \tabularnewline
Winsorized Mean ( 35 / 47 ) & 123.996453900709 & 1.31325192147889 & 94.4193965169098 \tabularnewline
Winsorized Mean ( 36 / 47 ) & 123.868794326241 & 1.29983988365981 & 95.295425139193 \tabularnewline
Winsorized Mean ( 37 / 47 ) & 123.737588652482 & 1.27552620963115 & 97.0090521999259 \tabularnewline
Winsorized Mean ( 38 / 47 ) & 123.872340425532 & 1.23507589583520 & 100.295326662306 \tabularnewline
Winsorized Mean ( 39 / 47 ) & 123.927659574468 & 1.20206598007298 & 103.095555176550 \tabularnewline
Winsorized Mean ( 40 / 47 ) & 123.700709219858 & 1.16211014813880 & 106.444909217920 \tabularnewline
Winsorized Mean ( 41 / 47 ) & 123.729787234043 & 1.15357764483166 & 107.257441914192 \tabularnewline
Winsorized Mean ( 42 / 47 ) & 123.640425531915 & 1.12706502075817 & 109.701235735932 \tabularnewline
Winsorized Mean ( 43 / 47 ) & 123.518439716312 & 1.07930359683488 & 114.442720360181 \tabularnewline
Winsorized Mean ( 44 / 47 ) & 123.705673758865 & 1.06154709843616 & 116.533382212721 \tabularnewline
Winsorized Mean ( 45 / 47 ) & 123.705673758865 & 1.02470139127766 & 120.723632086243 \tabularnewline
Winsorized Mean ( 46 / 47 ) & 123.738297872340 & 0.990502855299827 & 124.924726072480 \tabularnewline
Winsorized Mean ( 47 / 47 ) & 123.438297872340 & 0.936189359203676 & 131.851848836797 \tabularnewline
Trimmed Mean ( 1 / 47 ) & 125.767625899281 & 2.01770399430658 & 62.3320498220566 \tabularnewline
Trimmed Mean ( 2 / 47 ) & 125.605839416058 & 1.98778439030371 & 63.188864963804 \tabularnewline
Trimmed Mean ( 3 / 47 ) & 125.511851851852 & 1.97039785805255 & 63.6987354299613 \tabularnewline
Trimmed Mean ( 4 / 47 ) & 125.428571428571 & 1.95417966146137 & 64.1847696515139 \tabularnewline
Trimmed Mean ( 5 / 47 ) & 125.343511450382 & 1.93692618058889 & 64.7125908599537 \tabularnewline
Trimmed Mean ( 6 / 47 ) & 125.258914728682 & 1.91847328459515 & 65.2909351068264 \tabularnewline
Trimmed Mean ( 7 / 47 ) & 125.169291338583 & 1.89845104630509 & 65.932324977353 \tabularnewline
Trimmed Mean ( 8 / 47 ) & 125.08 & 1.8780281354174 & 66.6017711029662 \tabularnewline
Trimmed Mean ( 9 / 47 ) & 124.985365853659 & 1.85689930095762 & 67.3086396172387 \tabularnewline
Trimmed Mean ( 10 / 47 ) & 124.898347107438 & 1.83700520726068 & 67.9901976400409 \tabularnewline
Trimmed Mean ( 11 / 47 ) & 124.849579831933 & 1.82333771539152 & 68.473096770844 \tabularnewline
Trimmed Mean ( 12 / 47 ) & 124.796581196581 & 1.80869788834877 & 68.9980244907083 \tabularnewline
Trimmed Mean ( 13 / 47 ) & 124.749565217391 & 1.79370727058791 & 69.5484526728281 \tabularnewline
Trimmed Mean ( 14 / 47 ) & 124.702654867257 & 1.78012292904303 & 70.052833336794 \tabularnewline
Trimmed Mean ( 15 / 47 ) & 124.651351351351 & 1.76522735778604 & 70.6148988692823 \tabularnewline
Trimmed Mean ( 16 / 47 ) & 124.6 & 1.74909859800372 & 71.2366930842027 \tabularnewline
Trimmed Mean ( 17 / 47 ) & 124.56261682243 & 1.73416686810717 & 71.8285068831865 \tabularnewline
Trimmed Mean ( 18 / 47 ) & 124.518095238095 & 1.71818424738775 & 72.4707466195242 \tabularnewline
Trimmed Mean ( 19 / 47 ) & 124.477669902913 & 1.70185726925971 & 73.1422500296158 \tabularnewline
Trimmed Mean ( 20 / 47 ) & 124.432673267327 & 1.68382350672621 & 73.8988811893096 \tabularnewline
Trimmed Mean ( 21 / 47 ) & 124.390909090909 & 1.66471505458578 & 74.7220425190789 \tabularnewline
Trimmed Mean ( 22 / 47 ) & 124.352577319588 & 1.64440965183781 & 75.6214105047423 \tabularnewline
Trimmed Mean ( 23 / 47 ) & 124.311578947368 & 1.62229211931712 & 76.6271237264567 \tabularnewline
Trimmed Mean ( 24 / 47 ) & 124.256989247312 & 1.60125914533314 & 77.5995500849806 \tabularnewline
Trimmed Mean ( 25 / 47 ) & 124.198901098901 & 1.58077467794465 & 78.5683771582089 \tabularnewline
Trimmed Mean ( 26 / 47 ) & 124.126966292135 & 1.56133599261364 & 79.5004834829623 \tabularnewline
Trimmed Mean ( 27 / 47 ) & 124.034482758621 & 1.54217448170218 & 80.4283070627114 \tabularnewline
Trimmed Mean ( 28 / 47 ) & 123.934117647059 & 1.52096419453836 & 81.4839153295618 \tabularnewline
Trimmed Mean ( 29 / 47 ) & 123.842168674699 & 1.49941326607050 & 82.5937528212293 \tabularnewline
Trimmed Mean ( 30 / 47 ) & 123.749382716049 & 1.47517013400128 & 83.8882104943307 \tabularnewline
Trimmed Mean ( 31 / 47 ) & 123.650632911392 & 1.44816851889870 & 85.3841464565368 \tabularnewline
Trimmed Mean ( 32 / 47 ) & 123.570129870130 & 1.42299380301336 & 86.8381363351372 \tabularnewline
Trimmed Mean ( 33 / 47 ) & 123.476 & 1.39630637594172 & 88.4304491675213 \tabularnewline
Trimmed Mean ( 34 / 47 ) & 123.439726027397 & 1.38052024545834 & 89.4153681798523 \tabularnewline
Trimmed Mean ( 35 / 47 ) & 123.401408450704 & 1.36445018880772 & 90.4403909083225 \tabularnewline
Trimmed Mean ( 36 / 47 ) & 123.366666666667 & 1.3493496691725 & 91.426758745435 \tabularnewline
Trimmed Mean ( 37 / 47 ) & 123.337313432836 & 1.33260411281353 & 92.5536040650762 \tabularnewline
Trimmed Mean ( 38 / 47 ) & 123.313846153846 & 1.31525055547171 & 93.7569238354134 \tabularnewline
Trimmed Mean ( 39 / 47 ) & 123.280952380952 & 1.29910532280811 & 94.896811071847 \tabularnewline
Trimmed Mean ( 40 / 47 ) & 123.242622950820 & 1.28336447130572 & 96.0308826575436 \tabularnewline
Trimmed Mean ( 41 / 47 ) & 123.215254237288 & 1.26910372926106 & 97.0884029385295 \tabularnewline
Trimmed Mean ( 42 / 47 ) & 123.184210526316 & 1.25210546858949 & 98.3816568304618 \tabularnewline
Trimmed Mean ( 43 / 47 ) & 123.156363636364 & 1.23442420671761 & 99.7682668293116 \tabularnewline
Trimmed Mean ( 44 / 47 ) & 123.133962264151 & 1.21906107066954 & 101.007213852316 \tabularnewline
Trimmed Mean ( 45 / 47 ) & 123.098039215686 & 1.20165405675931 & 102.440497348850 \tabularnewline
Trimmed Mean ( 46 / 47 ) & 123.059183673469 & 1.18488897829240 & 103.857142675777 \tabularnewline
Trimmed Mean ( 47 / 47 ) & 123.014893617021 & 1.16838154592122 & 105.286577014557 \tabularnewline
Median & 122.1 &  &  \tabularnewline
Midrange & 137.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 123.115714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 123.401408450704 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 123.401408450704 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 123.401408450704 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 123.401408450704 &  &  \tabularnewline
Midmean - Closest Observation & 123.15 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 123.401408450704 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 123.401408450704 &  &  \tabularnewline
Number of observations & 141 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2913&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]125.928368794326[/C][C]2.05186655484876[/C][C]61.3725919440254[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]123.637560644502[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]121.419074567177[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]128.247323392915[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 47 )[/C][C]125.924822695035[/C][C]2.04505189179892[/C][C]61.5753679405497[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 47 )[/C][C]125.785815602837[/C][C]2.01798513714519[/C][C]62.3323796035406[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 47 )[/C][C]125.747517730496[/C][C]2.01055033410202[/C][C]62.5438297154892[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 47 )[/C][C]125.744680851064[/C][C]2.00850936110069[/C][C]62.6059720140683[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 47 )[/C][C]125.730496453901[/C][C]2.00627029831252[/C][C]62.6687722784179[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 47 )[/C][C]125.743262411348[/C][C]2.00472954083062[/C][C]62.7233049896836[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 47 )[/C][C]125.723404255319[/C][C]1.99614512954711[/C][C]62.9830979693562[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 47 )[/C][C]125.740425531915[/C][C]1.98793523618499[/C][C]63.251771608627[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 47 )[/C][C]125.657446808511[/C][C]1.96673223854141[/C][C]63.8914867748862[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 47 )[/C][C]125.309929078014[/C][C]1.91151427768772[/C][C]65.5553194348078[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 47 )[/C][C]125.333333333333[/C][C]1.90680875332305[/C][C]65.7293675178023[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 47 )[/C][C]125.256737588652[/C][C]1.89649313890171[/C][C]66.046501840334[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 47 )[/C][C]125.238297872340[/C][C]1.87122877333654[/C][C]66.9283733004121[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 47 )[/C][C]125.268085106383[/C][C]1.8678369610376[/C][C]67.0658562387563[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 47 )[/C][C]125.246808510638[/C][C]1.86246384764393[/C][C]67.2479139227744[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 47 )[/C][C]125.053900709220[/C][C]1.83501420166012[/C][C]68.1487372664936[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 47 )[/C][C]125.126241134752[/C][C]1.8268327171595[/C][C]68.4935407382607[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 47 )[/C][C]125.049645390071[/C][C]1.81116866672453[/C][C]69.0436223238234[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 47 )[/C][C]125.090070921986[/C][C]1.80664800280605[/C][C]69.2387619102881[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 47 )[/C][C]125.019148936170[/C][C]1.79451768824612[/C][C]69.6672703507083[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 47 )[/C][C]124.944680851064[/C][C]1.78189118525261[/C][C]70.1191418898852[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 47 )[/C][C]124.960283687943[/C][C]1.77287420813918[/C][C]70.4845742096402[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 47 )[/C][C]125.139716312057[/C][C]1.73439777524906[/C][C]72.1516817525247[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 47 )[/C][C]125.156737588652[/C][C]1.70152512342842[/C][C]73.5556212866684[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 47 )[/C][C]125.334042553191[/C][C]1.66305946922032[/C][C]75.3635362251665[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 47 )[/C][C]125.610638297872[/C][C]1.63105335837921[/C][C]77.0119736749094[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 47 )[/C][C]125.668085106383[/C][C]1.62118113944073[/C][C]77.5163749744432[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 47 )[/C][C]125.449645390071[/C][C]1.59489453431762[/C][C]78.657016304683[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 47 )[/C][C]125.387943262411[/C][C]1.58754603286371[/C][C]78.9822409346009[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 47 )[/C][C]125.409219858156[/C][C]1.57619509690097[/C][C]79.5645285946702[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 47 )[/C][C]125.013475177305[/C][C]1.52507153314654[/C][C]81.9722042279395[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 47 )[/C][C]125.172340425532[/C][C]1.49971125433731[/C][C]83.4642935855293[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 47 )[/C][C]124.095744680851[/C][C]1.37428654137774[/C][C]90.2983045707802[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 47 )[/C][C]124.095744680851[/C][C]1.34930687761914[/C][C]91.9699934382749[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 47 )[/C][C]123.996453900709[/C][C]1.31325192147889[/C][C]94.4193965169098[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 47 )[/C][C]123.868794326241[/C][C]1.29983988365981[/C][C]95.295425139193[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 47 )[/C][C]123.737588652482[/C][C]1.27552620963115[/C][C]97.0090521999259[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 47 )[/C][C]123.872340425532[/C][C]1.23507589583520[/C][C]100.295326662306[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 47 )[/C][C]123.927659574468[/C][C]1.20206598007298[/C][C]103.095555176550[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 47 )[/C][C]123.700709219858[/C][C]1.16211014813880[/C][C]106.444909217920[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 47 )[/C][C]123.729787234043[/C][C]1.15357764483166[/C][C]107.257441914192[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 47 )[/C][C]123.640425531915[/C][C]1.12706502075817[/C][C]109.701235735932[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 47 )[/C][C]123.518439716312[/C][C]1.07930359683488[/C][C]114.442720360181[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 47 )[/C][C]123.705673758865[/C][C]1.06154709843616[/C][C]116.533382212721[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 47 )[/C][C]123.705673758865[/C][C]1.02470139127766[/C][C]120.723632086243[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 47 )[/C][C]123.738297872340[/C][C]0.990502855299827[/C][C]124.924726072480[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 47 )[/C][C]123.438297872340[/C][C]0.936189359203676[/C][C]131.851848836797[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 47 )[/C][C]125.767625899281[/C][C]2.01770399430658[/C][C]62.3320498220566[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 47 )[/C][C]125.605839416058[/C][C]1.98778439030371[/C][C]63.188864963804[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 47 )[/C][C]125.511851851852[/C][C]1.97039785805255[/C][C]63.6987354299613[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 47 )[/C][C]125.428571428571[/C][C]1.95417966146137[/C][C]64.1847696515139[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 47 )[/C][C]125.343511450382[/C][C]1.93692618058889[/C][C]64.7125908599537[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 47 )[/C][C]125.258914728682[/C][C]1.91847328459515[/C][C]65.2909351068264[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 47 )[/C][C]125.169291338583[/C][C]1.89845104630509[/C][C]65.932324977353[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 47 )[/C][C]125.08[/C][C]1.8780281354174[/C][C]66.6017711029662[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 47 )[/C][C]124.985365853659[/C][C]1.85689930095762[/C][C]67.3086396172387[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 47 )[/C][C]124.898347107438[/C][C]1.83700520726068[/C][C]67.9901976400409[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 47 )[/C][C]124.849579831933[/C][C]1.82333771539152[/C][C]68.473096770844[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 47 )[/C][C]124.796581196581[/C][C]1.80869788834877[/C][C]68.9980244907083[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 47 )[/C][C]124.749565217391[/C][C]1.79370727058791[/C][C]69.5484526728281[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 47 )[/C][C]124.702654867257[/C][C]1.78012292904303[/C][C]70.052833336794[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 47 )[/C][C]124.651351351351[/C][C]1.76522735778604[/C][C]70.6148988692823[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 47 )[/C][C]124.6[/C][C]1.74909859800372[/C][C]71.2366930842027[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 47 )[/C][C]124.56261682243[/C][C]1.73416686810717[/C][C]71.8285068831865[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 47 )[/C][C]124.518095238095[/C][C]1.71818424738775[/C][C]72.4707466195242[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 47 )[/C][C]124.477669902913[/C][C]1.70185726925971[/C][C]73.1422500296158[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 47 )[/C][C]124.432673267327[/C][C]1.68382350672621[/C][C]73.8988811893096[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 47 )[/C][C]124.390909090909[/C][C]1.66471505458578[/C][C]74.7220425190789[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 47 )[/C][C]124.352577319588[/C][C]1.64440965183781[/C][C]75.6214105047423[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 47 )[/C][C]124.311578947368[/C][C]1.62229211931712[/C][C]76.6271237264567[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 47 )[/C][C]124.256989247312[/C][C]1.60125914533314[/C][C]77.5995500849806[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 47 )[/C][C]124.198901098901[/C][C]1.58077467794465[/C][C]78.5683771582089[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 47 )[/C][C]124.126966292135[/C][C]1.56133599261364[/C][C]79.5004834829623[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 47 )[/C][C]124.034482758621[/C][C]1.54217448170218[/C][C]80.4283070627114[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 47 )[/C][C]123.934117647059[/C][C]1.52096419453836[/C][C]81.4839153295618[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 47 )[/C][C]123.842168674699[/C][C]1.49941326607050[/C][C]82.5937528212293[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 47 )[/C][C]123.749382716049[/C][C]1.47517013400128[/C][C]83.8882104943307[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 47 )[/C][C]123.650632911392[/C][C]1.44816851889870[/C][C]85.3841464565368[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 47 )[/C][C]123.570129870130[/C][C]1.42299380301336[/C][C]86.8381363351372[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 47 )[/C][C]123.476[/C][C]1.39630637594172[/C][C]88.4304491675213[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 47 )[/C][C]123.439726027397[/C][C]1.38052024545834[/C][C]89.4153681798523[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 47 )[/C][C]123.401408450704[/C][C]1.36445018880772[/C][C]90.4403909083225[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 47 )[/C][C]123.366666666667[/C][C]1.3493496691725[/C][C]91.426758745435[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 47 )[/C][C]123.337313432836[/C][C]1.33260411281353[/C][C]92.5536040650762[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 47 )[/C][C]123.313846153846[/C][C]1.31525055547171[/C][C]93.7569238354134[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 47 )[/C][C]123.280952380952[/C][C]1.29910532280811[/C][C]94.896811071847[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 47 )[/C][C]123.242622950820[/C][C]1.28336447130572[/C][C]96.0308826575436[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 47 )[/C][C]123.215254237288[/C][C]1.26910372926106[/C][C]97.0884029385295[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 47 )[/C][C]123.184210526316[/C][C]1.25210546858949[/C][C]98.3816568304618[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 47 )[/C][C]123.156363636364[/C][C]1.23442420671761[/C][C]99.7682668293116[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 47 )[/C][C]123.133962264151[/C][C]1.21906107066954[/C][C]101.007213852316[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 47 )[/C][C]123.098039215686[/C][C]1.20165405675931[/C][C]102.440497348850[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 47 )[/C][C]123.059183673469[/C][C]1.18488897829240[/C][C]103.857142675777[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 47 )[/C][C]123.014893617021[/C][C]1.16838154592122[/C][C]105.286577014557[/C][/ROW]
[ROW][C]Median[/C][C]122.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]137.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]123.115714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]123.401408450704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]123.401408450704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]123.401408450704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]123.401408450704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]123.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]123.401408450704[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]123.401408450704[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]141[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2913&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 Mean125.9283687943262.0518665548487661.3725919440254
Geometric Mean123.637560644502
Harmonic Mean121.419074567177
Quadratic Mean128.247323392915
Winsorized Mean ( 1 / 47 )125.9248226950352.0450518917989261.5753679405497
Winsorized Mean ( 2 / 47 )125.7858156028372.0179851371451962.3323796035406
Winsorized Mean ( 3 / 47 )125.7475177304962.0105503341020262.5438297154892
Winsorized Mean ( 4 / 47 )125.7446808510642.0085093611006962.6059720140683
Winsorized Mean ( 5 / 47 )125.7304964539012.0062702983125262.6687722784179
Winsorized Mean ( 6 / 47 )125.7432624113482.0047295408306262.7233049896836
Winsorized Mean ( 7 / 47 )125.7234042553191.9961451295471162.9830979693562
Winsorized Mean ( 8 / 47 )125.7404255319151.9879352361849963.251771608627
Winsorized Mean ( 9 / 47 )125.6574468085111.9667322385414163.8914867748862
Winsorized Mean ( 10 / 47 )125.3099290780141.9115142776877265.5553194348078
Winsorized Mean ( 11 / 47 )125.3333333333331.9068087533230565.7293675178023
Winsorized Mean ( 12 / 47 )125.2567375886521.8964931389017166.046501840334
Winsorized Mean ( 13 / 47 )125.2382978723401.8712287733365466.9283733004121
Winsorized Mean ( 14 / 47 )125.2680851063831.867836961037667.0658562387563
Winsorized Mean ( 15 / 47 )125.2468085106381.8624638476439367.2479139227744
Winsorized Mean ( 16 / 47 )125.0539007092201.8350142016601268.1487372664936
Winsorized Mean ( 17 / 47 )125.1262411347521.826832717159568.4935407382607
Winsorized Mean ( 18 / 47 )125.0496453900711.8111686667245369.0436223238234
Winsorized Mean ( 19 / 47 )125.0900709219861.8066480028060569.2387619102881
Winsorized Mean ( 20 / 47 )125.0191489361701.7945176882461269.6672703507083
Winsorized Mean ( 21 / 47 )124.9446808510641.7818911852526170.1191418898852
Winsorized Mean ( 22 / 47 )124.9602836879431.7728742081391870.4845742096402
Winsorized Mean ( 23 / 47 )125.1397163120571.7343977752490672.1516817525247
Winsorized Mean ( 24 / 47 )125.1567375886521.7015251234284273.5556212866684
Winsorized Mean ( 25 / 47 )125.3340425531911.6630594692203275.3635362251665
Winsorized Mean ( 26 / 47 )125.6106382978721.6310533583792177.0119736749094
Winsorized Mean ( 27 / 47 )125.6680851063831.6211811394407377.5163749744432
Winsorized Mean ( 28 / 47 )125.4496453900711.5948945343176278.657016304683
Winsorized Mean ( 29 / 47 )125.3879432624111.5875460328637178.9822409346009
Winsorized Mean ( 30 / 47 )125.4092198581561.5761950969009779.5645285946702
Winsorized Mean ( 31 / 47 )125.0134751773051.5250715331465481.9722042279395
Winsorized Mean ( 32 / 47 )125.1723404255321.4997112543373183.4642935855293
Winsorized Mean ( 33 / 47 )124.0957446808511.3742865413777490.2983045707802
Winsorized Mean ( 34 / 47 )124.0957446808511.3493068776191491.9699934382749
Winsorized Mean ( 35 / 47 )123.9964539007091.3132519214788994.4193965169098
Winsorized Mean ( 36 / 47 )123.8687943262411.2998398836598195.295425139193
Winsorized Mean ( 37 / 47 )123.7375886524821.2755262096311597.0090521999259
Winsorized Mean ( 38 / 47 )123.8723404255321.23507589583520100.295326662306
Winsorized Mean ( 39 / 47 )123.9276595744681.20206598007298103.095555176550
Winsorized Mean ( 40 / 47 )123.7007092198581.16211014813880106.444909217920
Winsorized Mean ( 41 / 47 )123.7297872340431.15357764483166107.257441914192
Winsorized Mean ( 42 / 47 )123.6404255319151.12706502075817109.701235735932
Winsorized Mean ( 43 / 47 )123.5184397163121.07930359683488114.442720360181
Winsorized Mean ( 44 / 47 )123.7056737588651.06154709843616116.533382212721
Winsorized Mean ( 45 / 47 )123.7056737588651.02470139127766120.723632086243
Winsorized Mean ( 46 / 47 )123.7382978723400.990502855299827124.924726072480
Winsorized Mean ( 47 / 47 )123.4382978723400.936189359203676131.851848836797
Trimmed Mean ( 1 / 47 )125.7676258992812.0177039943065862.3320498220566
Trimmed Mean ( 2 / 47 )125.6058394160581.9877843903037163.188864963804
Trimmed Mean ( 3 / 47 )125.5118518518521.9703978580525563.6987354299613
Trimmed Mean ( 4 / 47 )125.4285714285711.9541796614613764.1847696515139
Trimmed Mean ( 5 / 47 )125.3435114503821.9369261805888964.7125908599537
Trimmed Mean ( 6 / 47 )125.2589147286821.9184732845951565.2909351068264
Trimmed Mean ( 7 / 47 )125.1692913385831.8984510463050965.932324977353
Trimmed Mean ( 8 / 47 )125.081.878028135417466.6017711029662
Trimmed Mean ( 9 / 47 )124.9853658536591.8568993009576267.3086396172387
Trimmed Mean ( 10 / 47 )124.8983471074381.8370052072606867.9901976400409
Trimmed Mean ( 11 / 47 )124.8495798319331.8233377153915268.473096770844
Trimmed Mean ( 12 / 47 )124.7965811965811.8086978883487768.9980244907083
Trimmed Mean ( 13 / 47 )124.7495652173911.7937072705879169.5484526728281
Trimmed Mean ( 14 / 47 )124.7026548672571.7801229290430370.052833336794
Trimmed Mean ( 15 / 47 )124.6513513513511.7652273577860470.6148988692823
Trimmed Mean ( 16 / 47 )124.61.7490985980037271.2366930842027
Trimmed Mean ( 17 / 47 )124.562616822431.7341668681071771.8285068831865
Trimmed Mean ( 18 / 47 )124.5180952380951.7181842473877572.4707466195242
Trimmed Mean ( 19 / 47 )124.4776699029131.7018572692597173.1422500296158
Trimmed Mean ( 20 / 47 )124.4326732673271.6838235067262173.8988811893096
Trimmed Mean ( 21 / 47 )124.3909090909091.6647150545857874.7220425190789
Trimmed Mean ( 22 / 47 )124.3525773195881.6444096518378175.6214105047423
Trimmed Mean ( 23 / 47 )124.3115789473681.6222921193171276.6271237264567
Trimmed Mean ( 24 / 47 )124.2569892473121.6012591453331477.5995500849806
Trimmed Mean ( 25 / 47 )124.1989010989011.5807746779446578.5683771582089
Trimmed Mean ( 26 / 47 )124.1269662921351.5613359926136479.5004834829623
Trimmed Mean ( 27 / 47 )124.0344827586211.5421744817021880.4283070627114
Trimmed Mean ( 28 / 47 )123.9341176470591.5209641945383681.4839153295618
Trimmed Mean ( 29 / 47 )123.8421686746991.4994132660705082.5937528212293
Trimmed Mean ( 30 / 47 )123.7493827160491.4751701340012883.8882104943307
Trimmed Mean ( 31 / 47 )123.6506329113921.4481685188987085.3841464565368
Trimmed Mean ( 32 / 47 )123.5701298701301.4229938030133686.8381363351372
Trimmed Mean ( 33 / 47 )123.4761.3963063759417288.4304491675213
Trimmed Mean ( 34 / 47 )123.4397260273971.3805202454583489.4153681798523
Trimmed Mean ( 35 / 47 )123.4014084507041.3644501888077290.4403909083225
Trimmed Mean ( 36 / 47 )123.3666666666671.349349669172591.426758745435
Trimmed Mean ( 37 / 47 )123.3373134328361.3326041128135392.5536040650762
Trimmed Mean ( 38 / 47 )123.3138461538461.3152505554717193.7569238354134
Trimmed Mean ( 39 / 47 )123.2809523809521.2991053228081194.896811071847
Trimmed Mean ( 40 / 47 )123.2426229508201.2833644713057296.0308826575436
Trimmed Mean ( 41 / 47 )123.2152542372881.2691037292610697.0884029385295
Trimmed Mean ( 42 / 47 )123.1842105263161.2521054685894998.3816568304618
Trimmed Mean ( 43 / 47 )123.1563636363641.2344242067176199.7682668293116
Trimmed Mean ( 44 / 47 )123.1339622641511.21906107066954101.007213852316
Trimmed Mean ( 45 / 47 )123.0980392156861.20165405675931102.440497348850
Trimmed Mean ( 46 / 47 )123.0591836734691.18488897829240103.857142675777
Trimmed Mean ( 47 / 47 )123.0148936170211.16838154592122105.286577014557
Median122.1
Midrange137.1
Midmean - Weighted Average at Xnp123.115714285714
Midmean - Weighted Average at X(n+1)p123.401408450704
Midmean - Empirical Distribution Function123.401408450704
Midmean - Empirical Distribution Function - Averaging123.401408450704
Midmean - Empirical Distribution Function - Interpolation123.401408450704
Midmean - Closest Observation123.15
Midmean - True Basic - Statistics Graphics Toolkit123.401408450704
Midmean - MS Excel (old versions)123.401408450704
Number of observations141



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')