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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Dec 2010 12:38:38 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292848653rsceu3ls0ca6fbw.htm/, Retrieved Mon, 20 May 2024 10:37:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112879, Retrieved Mon, 20 May 2024 10:37:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D    [Central Tendency] [Central Tendency ...] [2010-12-20 12:38:38] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
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Post a new message
Dataseries X:
25,00
25,09
25,03
25,21
25,33
25,23
25,13
25,03
25,03
25,15
25,18
24,90
25,18
25,25
25,28
25,32
25,27
25,22
25,14
25,41
25,72
25,66
25,65
25,27
23,90
24,06
24,33
24,39
24,39
24,49
24,83
25,08
25,11
25,13
25,17
25,11
25,35
25,36
25,35
25,34
25,39
25,58
25,71
25,66
25,74
25,73
25,72
25,55
25,71
25,92
25,93
26,00
26,02
26,08
26,17
26,18
26,21
26,28
26,34
26,17
26,38
26,36
26,27
26,26
26,49
26,99
27,14
27,10
27,01
26,93
26,97
26,35
26,93




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112879&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112879&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean25.5936986301370.0848511335958488301.630603452411
Geometric Mean25.5836062590385
Harmonic Mean25.5735472297559
Quadratic Mean25.6038237191459
Winsorized Mean ( 1 / 24 )25.59534246575340.0841320359588017304.228254719607
Winsorized Mean ( 2 / 24 )25.60027397260270.0817932977336025312.987429067621
Winsorized Mean ( 3 / 24 )25.60191780821920.0810752646391657315.779639106493
Winsorized Mean ( 4 / 24 )25.60082191780820.0808160324715277316.778999597978
Winsorized Mean ( 5 / 24 )25.60493150684930.0787874535340893324.987423229394
Winsorized Mean ( 6 / 24 )25.63287671232880.0739128408743759346.798694368886
Winsorized Mean ( 7 / 24 )25.5973972602740.0635615413254304402.718321905021
Winsorized Mean ( 8 / 24 )25.5963013698630.0596866841148713428.844418976285
Winsorized Mean ( 9 / 24 )25.59753424657530.0587346860840172435.816311505594
Winsorized Mean ( 10 / 24 )25.59616438356160.0584885834054324437.626676750463
Winsorized Mean ( 11 / 24 )25.59465753424660.0582197466173332439.621589260344
Winsorized Mean ( 12 / 24 )25.59301369863010.0554103568459503461.881409097993
Winsorized Mean ( 13 / 24 )25.59301369863010.0548766032837026466.373867316799
Winsorized Mean ( 14 / 24 )25.59493150684930.0540653683243007473.407142134371
Winsorized Mean ( 15 / 24 )25.58465753424660.0523347883169542488.865214841392
Winsorized Mean ( 16 / 24 )25.58246575342470.0507031159530504504.554114132024
Winsorized Mean ( 17 / 24 )25.58013698630140.0503229649843945508.31935268985
Winsorized Mean ( 18 / 24 )25.5826027397260.0500182719266867511.465145721612
Winsorized Mean ( 19 / 24 )25.56178082191780.045948213216442556.317189125667
Winsorized Mean ( 20 / 24 )25.55082191780820.0427256982404215598.019996631333
Winsorized Mean ( 21 / 24 )25.54794520547950.0414964371506639615.665993509776
Winsorized Mean ( 22 / 24 )25.52684931506850.0383585765168907665.479578050245
Winsorized Mean ( 23 / 24 )25.53315068493150.0367267444266014695.21954868501
Winsorized Mean ( 24 / 24 )25.47726027397260.028079212449151907.335286561533
Trimmed Mean ( 1 / 24 )25.59577464788730.0809671573061987316.125395771154
Trimmed Mean ( 2 / 24 )25.5962318840580.0771956531142163331.576077816021
Trimmed Mean ( 3 / 24 )25.59402985074630.074218393642271344.847531652439
Trimmed Mean ( 4 / 24 )25.59107692307690.0709804696448672360.536877976652
Trimmed Mean ( 5 / 24 )25.5882539682540.0671535750821607381.040829724216
Trimmed Mean ( 6 / 24 )25.5842622950820.0631744306616246404.978122115839
Trimmed Mean ( 7 / 24 )25.57423728813560.0597609710758561427.94213058676
Trimmed Mean ( 8 / 24 )25.570.0585085089028518437.030450433401
Trimmed Mean ( 9 / 24 )25.56563636363640.0578659565871131441.807893128823
Trimmed Mean ( 10 / 24 )25.56075471698110.0572272029871059446.653923008265
Trimmed Mean ( 11 / 24 )25.55568627450980.0564292059702092452.880486888323
Trimmed Mean ( 12 / 24 )25.55040816326530.0554319457610554460.932911743757
Trimmed Mean ( 13 / 24 )25.54489361702130.0547130030700403466.888896307159
Trimmed Mean ( 14 / 24 )25.53888888888890.0538312197936002474.425231061272
Trimmed Mean ( 15 / 24 )25.53209302325580.0527835989782831483.712621296637
Trimmed Mean ( 16 / 24 )25.52585365853660.0517521952047142493.232288167969
Trimmed Mean ( 17 / 24 )25.51923076923080.0506774412535669503.561942710251
Trimmed Mean ( 18 / 24 )25.51216216216220.0492376341316798518.143542273643
Trimmed Mean ( 19 / 24 )25.5040.0472401339128165539.879925977107
Trimmed Mean ( 20 / 24 )25.49727272727270.0456129814541319558.991583413871
Trimmed Mean ( 21 / 24 )25.49096774193550.0441827943904934576.943312291271
Trimmed Mean ( 22 / 24 )25.48413793103450.0423785347462165601.345423659548
Trimmed Mean ( 23 / 24 )25.47888888888890.0407596433744849625.100878699993
Trimmed Mean ( 24 / 24 )25.4720.0386910842443062658.342884349344
Median25.39
Midrange25.52
Midmean - Weighted Average at Xnp25.4938888888889
Midmean - Weighted Average at X(n+1)p25.5294736842105
Midmean - Empirical Distribution Function25.5294736842105
Midmean - Empirical Distribution Function - Averaging25.5294736842105
Midmean - Empirical Distribution Function - Interpolation25.5294736842105
Midmean - Closest Observation25.5095
Midmean - True Basic - Statistics Graphics Toolkit25.5294736842105
Midmean - MS Excel (old versions)25.5294736842105
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 25.593698630137 & 0.0848511335958488 & 301.630603452411 \tabularnewline
Geometric Mean & 25.5836062590385 &  &  \tabularnewline
Harmonic Mean & 25.5735472297559 &  &  \tabularnewline
Quadratic Mean & 25.6038237191459 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 25.5953424657534 & 0.0841320359588017 & 304.228254719607 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 25.6002739726027 & 0.0817932977336025 & 312.987429067621 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 25.6019178082192 & 0.0810752646391657 & 315.779639106493 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 25.6008219178082 & 0.0808160324715277 & 316.778999597978 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 25.6049315068493 & 0.0787874535340893 & 324.987423229394 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 25.6328767123288 & 0.0739128408743759 & 346.798694368886 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 25.597397260274 & 0.0635615413254304 & 402.718321905021 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 25.596301369863 & 0.0596866841148713 & 428.844418976285 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 25.5975342465753 & 0.0587346860840172 & 435.816311505594 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 25.5961643835616 & 0.0584885834054324 & 437.626676750463 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 25.5946575342466 & 0.0582197466173332 & 439.621589260344 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 25.5930136986301 & 0.0554103568459503 & 461.881409097993 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 25.5930136986301 & 0.0548766032837026 & 466.373867316799 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 25.5949315068493 & 0.0540653683243007 & 473.407142134371 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 25.5846575342466 & 0.0523347883169542 & 488.865214841392 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 25.5824657534247 & 0.0507031159530504 & 504.554114132024 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 25.5801369863014 & 0.0503229649843945 & 508.31935268985 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 25.582602739726 & 0.0500182719266867 & 511.465145721612 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 25.5617808219178 & 0.045948213216442 & 556.317189125667 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 25.5508219178082 & 0.0427256982404215 & 598.019996631333 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 25.5479452054795 & 0.0414964371506639 & 615.665993509776 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 25.5268493150685 & 0.0383585765168907 & 665.479578050245 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 25.5331506849315 & 0.0367267444266014 & 695.21954868501 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 25.4772602739726 & 0.028079212449151 & 907.335286561533 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 25.5957746478873 & 0.0809671573061987 & 316.125395771154 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 25.596231884058 & 0.0771956531142163 & 331.576077816021 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 25.5940298507463 & 0.074218393642271 & 344.847531652439 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 25.5910769230769 & 0.0709804696448672 & 360.536877976652 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 25.588253968254 & 0.0671535750821607 & 381.040829724216 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 25.584262295082 & 0.0631744306616246 & 404.978122115839 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 25.5742372881356 & 0.0597609710758561 & 427.94213058676 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 25.57 & 0.0585085089028518 & 437.030450433401 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 25.5656363636364 & 0.0578659565871131 & 441.807893128823 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 25.5607547169811 & 0.0572272029871059 & 446.653923008265 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 25.5556862745098 & 0.0564292059702092 & 452.880486888323 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 25.5504081632653 & 0.0554319457610554 & 460.932911743757 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 25.5448936170213 & 0.0547130030700403 & 466.888896307159 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 25.5388888888889 & 0.0538312197936002 & 474.425231061272 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 25.5320930232558 & 0.0527835989782831 & 483.712621296637 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 25.5258536585366 & 0.0517521952047142 & 493.232288167969 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 25.5192307692308 & 0.0506774412535669 & 503.561942710251 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 25.5121621621622 & 0.0492376341316798 & 518.143542273643 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 25.504 & 0.0472401339128165 & 539.879925977107 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 25.4972727272727 & 0.0456129814541319 & 558.991583413871 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 25.4909677419355 & 0.0441827943904934 & 576.943312291271 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 25.4841379310345 & 0.0423785347462165 & 601.345423659548 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 25.4788888888889 & 0.0407596433744849 & 625.100878699993 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 25.472 & 0.0386910842443062 & 658.342884349344 \tabularnewline
Median & 25.39 &  &  \tabularnewline
Midrange & 25.52 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 25.4938888888889 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 25.5294736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 25.5294736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 25.5294736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 25.5294736842105 &  &  \tabularnewline
Midmean - Closest Observation & 25.5095 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 25.5294736842105 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 25.5294736842105 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112879&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]25.593698630137[/C][C]0.0848511335958488[/C][C]301.630603452411[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]25.5836062590385[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]25.5735472297559[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]25.6038237191459[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]25.5953424657534[/C][C]0.0841320359588017[/C][C]304.228254719607[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]25.6002739726027[/C][C]0.0817932977336025[/C][C]312.987429067621[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]25.6019178082192[/C][C]0.0810752646391657[/C][C]315.779639106493[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]25.6008219178082[/C][C]0.0808160324715277[/C][C]316.778999597978[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]25.6049315068493[/C][C]0.0787874535340893[/C][C]324.987423229394[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]25.6328767123288[/C][C]0.0739128408743759[/C][C]346.798694368886[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]25.597397260274[/C][C]0.0635615413254304[/C][C]402.718321905021[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]25.596301369863[/C][C]0.0596866841148713[/C][C]428.844418976285[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]25.5975342465753[/C][C]0.0587346860840172[/C][C]435.816311505594[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]25.5961643835616[/C][C]0.0584885834054324[/C][C]437.626676750463[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]25.5946575342466[/C][C]0.0582197466173332[/C][C]439.621589260344[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]25.5930136986301[/C][C]0.0554103568459503[/C][C]461.881409097993[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]25.5930136986301[/C][C]0.0548766032837026[/C][C]466.373867316799[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]25.5949315068493[/C][C]0.0540653683243007[/C][C]473.407142134371[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]25.5846575342466[/C][C]0.0523347883169542[/C][C]488.865214841392[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]25.5824657534247[/C][C]0.0507031159530504[/C][C]504.554114132024[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]25.5801369863014[/C][C]0.0503229649843945[/C][C]508.31935268985[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]25.582602739726[/C][C]0.0500182719266867[/C][C]511.465145721612[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]25.5617808219178[/C][C]0.045948213216442[/C][C]556.317189125667[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]25.5508219178082[/C][C]0.0427256982404215[/C][C]598.019996631333[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]25.5479452054795[/C][C]0.0414964371506639[/C][C]615.665993509776[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]25.5268493150685[/C][C]0.0383585765168907[/C][C]665.479578050245[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]25.5331506849315[/C][C]0.0367267444266014[/C][C]695.21954868501[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]25.4772602739726[/C][C]0.028079212449151[/C][C]907.335286561533[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]25.5957746478873[/C][C]0.0809671573061987[/C][C]316.125395771154[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]25.596231884058[/C][C]0.0771956531142163[/C][C]331.576077816021[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]25.5940298507463[/C][C]0.074218393642271[/C][C]344.847531652439[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]25.5910769230769[/C][C]0.0709804696448672[/C][C]360.536877976652[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]25.588253968254[/C][C]0.0671535750821607[/C][C]381.040829724216[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]25.584262295082[/C][C]0.0631744306616246[/C][C]404.978122115839[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]25.5742372881356[/C][C]0.0597609710758561[/C][C]427.94213058676[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]25.57[/C][C]0.0585085089028518[/C][C]437.030450433401[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]25.5656363636364[/C][C]0.0578659565871131[/C][C]441.807893128823[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]25.5607547169811[/C][C]0.0572272029871059[/C][C]446.653923008265[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]25.5556862745098[/C][C]0.0564292059702092[/C][C]452.880486888323[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]25.5504081632653[/C][C]0.0554319457610554[/C][C]460.932911743757[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]25.5448936170213[/C][C]0.0547130030700403[/C][C]466.888896307159[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]25.5388888888889[/C][C]0.0538312197936002[/C][C]474.425231061272[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]25.5320930232558[/C][C]0.0527835989782831[/C][C]483.712621296637[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]25.5258536585366[/C][C]0.0517521952047142[/C][C]493.232288167969[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]25.5192307692308[/C][C]0.0506774412535669[/C][C]503.561942710251[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]25.5121621621622[/C][C]0.0492376341316798[/C][C]518.143542273643[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]25.504[/C][C]0.0472401339128165[/C][C]539.879925977107[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]25.4972727272727[/C][C]0.0456129814541319[/C][C]558.991583413871[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]25.4909677419355[/C][C]0.0441827943904934[/C][C]576.943312291271[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]25.4841379310345[/C][C]0.0423785347462165[/C][C]601.345423659548[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]25.4788888888889[/C][C]0.0407596433744849[/C][C]625.100878699993[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]25.472[/C][C]0.0386910842443062[/C][C]658.342884349344[/C][/ROW]
[ROW][C]Median[/C][C]25.39[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]25.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]25.4938888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]25.5294736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]25.5294736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]25.5294736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]25.5294736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]25.5095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]25.5294736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]25.5294736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112879&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 Mean25.5936986301370.0848511335958488301.630603452411
Geometric Mean25.5836062590385
Harmonic Mean25.5735472297559
Quadratic Mean25.6038237191459
Winsorized Mean ( 1 / 24 )25.59534246575340.0841320359588017304.228254719607
Winsorized Mean ( 2 / 24 )25.60027397260270.0817932977336025312.987429067621
Winsorized Mean ( 3 / 24 )25.60191780821920.0810752646391657315.779639106493
Winsorized Mean ( 4 / 24 )25.60082191780820.0808160324715277316.778999597978
Winsorized Mean ( 5 / 24 )25.60493150684930.0787874535340893324.987423229394
Winsorized Mean ( 6 / 24 )25.63287671232880.0739128408743759346.798694368886
Winsorized Mean ( 7 / 24 )25.5973972602740.0635615413254304402.718321905021
Winsorized Mean ( 8 / 24 )25.5963013698630.0596866841148713428.844418976285
Winsorized Mean ( 9 / 24 )25.59753424657530.0587346860840172435.816311505594
Winsorized Mean ( 10 / 24 )25.59616438356160.0584885834054324437.626676750463
Winsorized Mean ( 11 / 24 )25.59465753424660.0582197466173332439.621589260344
Winsorized Mean ( 12 / 24 )25.59301369863010.0554103568459503461.881409097993
Winsorized Mean ( 13 / 24 )25.59301369863010.0548766032837026466.373867316799
Winsorized Mean ( 14 / 24 )25.59493150684930.0540653683243007473.407142134371
Winsorized Mean ( 15 / 24 )25.58465753424660.0523347883169542488.865214841392
Winsorized Mean ( 16 / 24 )25.58246575342470.0507031159530504504.554114132024
Winsorized Mean ( 17 / 24 )25.58013698630140.0503229649843945508.31935268985
Winsorized Mean ( 18 / 24 )25.5826027397260.0500182719266867511.465145721612
Winsorized Mean ( 19 / 24 )25.56178082191780.045948213216442556.317189125667
Winsorized Mean ( 20 / 24 )25.55082191780820.0427256982404215598.019996631333
Winsorized Mean ( 21 / 24 )25.54794520547950.0414964371506639615.665993509776
Winsorized Mean ( 22 / 24 )25.52684931506850.0383585765168907665.479578050245
Winsorized Mean ( 23 / 24 )25.53315068493150.0367267444266014695.21954868501
Winsorized Mean ( 24 / 24 )25.47726027397260.028079212449151907.335286561533
Trimmed Mean ( 1 / 24 )25.59577464788730.0809671573061987316.125395771154
Trimmed Mean ( 2 / 24 )25.5962318840580.0771956531142163331.576077816021
Trimmed Mean ( 3 / 24 )25.59402985074630.074218393642271344.847531652439
Trimmed Mean ( 4 / 24 )25.59107692307690.0709804696448672360.536877976652
Trimmed Mean ( 5 / 24 )25.5882539682540.0671535750821607381.040829724216
Trimmed Mean ( 6 / 24 )25.5842622950820.0631744306616246404.978122115839
Trimmed Mean ( 7 / 24 )25.57423728813560.0597609710758561427.94213058676
Trimmed Mean ( 8 / 24 )25.570.0585085089028518437.030450433401
Trimmed Mean ( 9 / 24 )25.56563636363640.0578659565871131441.807893128823
Trimmed Mean ( 10 / 24 )25.56075471698110.0572272029871059446.653923008265
Trimmed Mean ( 11 / 24 )25.55568627450980.0564292059702092452.880486888323
Trimmed Mean ( 12 / 24 )25.55040816326530.0554319457610554460.932911743757
Trimmed Mean ( 13 / 24 )25.54489361702130.0547130030700403466.888896307159
Trimmed Mean ( 14 / 24 )25.53888888888890.0538312197936002474.425231061272
Trimmed Mean ( 15 / 24 )25.53209302325580.0527835989782831483.712621296637
Trimmed Mean ( 16 / 24 )25.52585365853660.0517521952047142493.232288167969
Trimmed Mean ( 17 / 24 )25.51923076923080.0506774412535669503.561942710251
Trimmed Mean ( 18 / 24 )25.51216216216220.0492376341316798518.143542273643
Trimmed Mean ( 19 / 24 )25.5040.0472401339128165539.879925977107
Trimmed Mean ( 20 / 24 )25.49727272727270.0456129814541319558.991583413871
Trimmed Mean ( 21 / 24 )25.49096774193550.0441827943904934576.943312291271
Trimmed Mean ( 22 / 24 )25.48413793103450.0423785347462165601.345423659548
Trimmed Mean ( 23 / 24 )25.47888888888890.0407596433744849625.100878699993
Trimmed Mean ( 24 / 24 )25.4720.0386910842443062658.342884349344
Median25.39
Midrange25.52
Midmean - Weighted Average at Xnp25.4938888888889
Midmean - Weighted Average at X(n+1)p25.5294736842105
Midmean - Empirical Distribution Function25.5294736842105
Midmean - Empirical Distribution Function - Averaging25.5294736842105
Midmean - Empirical Distribution Function - Interpolation25.5294736842105
Midmean - Closest Observation25.5095
Midmean - True Basic - Statistics Graphics Toolkit25.5294736842105
Midmean - MS Excel (old versions)25.5294736842105
Number of observations73



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')