Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 01 Nov 2009 04:35:57 -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/2009/Nov/01/t1257075494vd24ppuempwto3q.htm/, Retrieved Tue, 07 May 2024 02:31:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52262, Retrieved Tue, 07 May 2024 02:31:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-11-01 11:35:57] [6fe3b5976049c9b6736c06f51fce3033] [Current]
Feedback Forum

Post a new message
Dataseries X:
23,98
24,24
24,92
25,46
25,84
26,08
26,18
26,34
26,42
26,38
26,04
25,58
25,65
25,56
25,62
25,62
25,69
25,68
25,68
25,83
25,93
26,11
24,72
24,62
24,65
25,24
25,56
25,9
25,87
25,78
25,78
25,74
25,78
25,73
24,67
24,31
24,56
25
25,38
25,99
26,22
26,19
26,22
26,22
26,61
26,72
25,46
25,48
25,59
25,88
26
26,97
27,2
27,19
27,19
27,19
27,26
26,9
26,11
25,87
26,02
26,31
26,37
26,52
26,86
26,92
26,98
26,98
27,03
26,75
26,39
26,3
26,3
26,52
26,53
26,98
27,22
27,34
27,41
27,47
27,46
27,53
27,21
26,91
26,95
26,91
27,39
27,62
27,79
27,88
27,9
28,09
28,46
28,73
27,93
27,61
27,65
28,19
28,98
28,99
29,02
29
29,04
29,19
29,23
29,26
29,02
28,47
28,53
28,48
28,68
28,89
29,2
29,21
29,15
29,22
29,34
29,13
28,84
28,76




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52262&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52262&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26.83016666666670.124173964404947216.069180002742
Geometric Mean26.7962066202645
Harmonic Mean26.7624926231037
Quadratic Mean26.8643392809129
Winsorized Mean ( 1 / 40 )26.83166666666670.123662555519938216.974868050019
Winsorized Mean ( 2 / 40 )26.83233333333330.123377522555348217.481537784130
Winsorized Mean ( 3 / 40 )26.83833333333330.122310410845959219.428036809837
Winsorized Mean ( 4 / 40 )26.840.121946399576814220.096698985308
Winsorized Mean ( 5 / 40 )26.84083333333330.121688263115301220.570436673103
Winsorized Mean ( 6 / 40 )26.84133333333330.121456147250556220.996087402324
Winsorized Mean ( 7 / 40 )26.84191666666670.120644354056595222.487963705911
Winsorized Mean ( 8 / 40 )26.85391666666670.118529582157389226.558772737500
Winsorized Mean ( 9 / 40 )26.85316666666670.116641192697092230.220268206638
Winsorized Mean ( 10 / 40 )26.87150.113836683965436236.053081168097
Winsorized Mean ( 11 / 40 )26.88433333333330.112341499507846239.309012707773
Winsorized Mean ( 12 / 40 )26.89033333333330.111139434298583241.951324505492
Winsorized Mean ( 13 / 40 )26.889250.110966858712379242.317844372758
Winsorized Mean ( 14 / 40 )26.89041666666670.110530006308624243.286122608034
Winsorized Mean ( 15 / 40 )26.88916666666670.107703139012417249.660009106761
Winsorized Mean ( 16 / 40 )26.88250.106668696365493252.018641981795
Winsorized Mean ( 17 / 40 )26.8740.104641605235291256.819454743385
Winsorized Mean ( 18 / 40 )26.8710.103806502281728258.856616968683
Winsorized Mean ( 19 / 40 )26.86783333333330.102130401028256263.073806259705
Winsorized Mean ( 20 / 40 )26.84283333333330.098465551095638272.611416222729
Winsorized Mean ( 21 / 40 )26.83933333333330.0966661885432009277.649649146336
Winsorized Mean ( 22 / 40 )26.8430.0958399108691476280.081646117653
Winsorized Mean ( 23 / 40 )26.84108333333330.0955667742733042280.862083474457
Winsorized Mean ( 24 / 40 )26.78908333333330.087890146278134304.801897229270
Winsorized Mean ( 25 / 40 )26.77658333333330.0842568847674714317.796977745263
Winsorized Mean ( 26 / 40 )26.74408333333330.0795851019792617336.043840721625
Winsorized Mean ( 27 / 40 )26.74633333333330.077794973422597343.805417710501
Winsorized Mean ( 28 / 40 )26.74166666666670.0772151250525531346.32679346781
Winsorized Mean ( 29 / 40 )26.71991666666670.074555592387219358.389167212187
Winsorized Mean ( 30 / 40 )26.69741666666670.069092607832166386.400477624434
Winsorized Mean ( 31 / 40 )26.692250.0679264166155532392.958311801895
Winsorized Mean ( 32 / 40 )26.69758333333330.0667819726753892399.772307761913
Winsorized Mean ( 33 / 40 )26.67558333333330.0642898935901577414.926543562006
Winsorized Mean ( 34 / 40 )26.66141666666670.0621114584837344429.251177118127
Winsorized Mean ( 35 / 40 )26.66433333333330.0611779483409828435.848766694764
Winsorized Mean ( 36 / 40 )26.65833333333330.0586072400826273454.864165173947
Winsorized Mean ( 37 / 40 )26.67066666666670.0560315454034492475.993772340694
Winsorized Mean ( 38 / 40 )26.6580.0540135111222507493.543179217955
Winsorized Mean ( 39 / 40 )26.63850.0506254508573485526.187906455618
Winsorized Mean ( 40 / 40 )26.63183333333330.0485756482623578548.254820800216
Trimmed Mean ( 1 / 40 )26.83305084745760.122081191441198219.796764191822
Trimmed Mean ( 2 / 40 )26.83448275862070.120328096249547223.010947526079
Trimmed Mean ( 3 / 40 )26.83561403508770.118547137992523226.370830114687
Trimmed Mean ( 4 / 40 )26.83464285714290.116996816042779229.362163559485
Trimmed Mean ( 5 / 40 )26.83318181818180.115382811507156232.557878142168
Trimmed Mean ( 6 / 40 )26.83148148148150.113648378226744236.092075400752
Trimmed Mean ( 7 / 40 )26.82962264150940.111761918409708240.060505611176
Trimmed Mean ( 8 / 40 )26.82759615384620.109818022396928244.291379213513
Trimmed Mean ( 9 / 40 )26.82372549019610.108037138646394248.282450148835
Trimmed Mean ( 10 / 40 )26.81980.106365956807979252.146464948532
Trimmed Mean ( 11 / 40 )26.81346938775510.104930632616428255.535192337697
Trimmed Mean ( 12 / 40 )26.80541666666670.103521007769958258.936975635256
Trimmed Mean ( 13 / 40 )26.79638297872340.102083852993284262.493843962632
Trimmed Mean ( 14 / 40 )26.78706521739130.100462087897463266.638547714951
Trimmed Mean ( 15 / 40 )26.77722222222220.0986610773517813271.406140506115
Trimmed Mean ( 16 / 40 )26.76704545454550.096986215489936275.988142431673
Trimmed Mean ( 17 / 40 )26.75697674418600.0952008561054636281.058152613088
Trimmed Mean ( 18 / 40 )26.74714285714290.0934198493720701286.311132344209
Trimmed Mean ( 19 / 40 )26.73707317073170.091466273166211292.316197492222
Trimmed Mean ( 20 / 40 )26.726750.0894216252198652298.884637069452
Trimmed Mean ( 21 / 40 )26.71782051282050.0875664720512504305.114730409411
Trimmed Mean ( 22 / 40 )26.70868421052630.08563638800803311.884758708201
Trimmed Mean ( 23 / 40 )26.69878378378380.0834664018234104319.874622608871
Trimmed Mean ( 24 / 40 )26.68847222222220.0809353718588314329.750412079068
Trimmed Mean ( 25 / 40 )26.68128571428570.0791141224154848337.250605829427
Trimmed Mean ( 26 / 40 )26.67455882352940.077463473457396344.350151535615
Trimmed Mean ( 27 / 40 )26.66969696969700.0761662914193456350.150919425271
Trimmed Mean ( 28 / 40 )26.6643750.0748354262487052356.306850065698
Trimmed Mean ( 29 / 40 )26.65903225806450.0732976046761755363.709460572996
Trimmed Mean ( 30 / 40 )26.65483333333330.0718325468254293371.069028056475
Trimmed Mean ( 31 / 40 )26.65189655172410.0708493356807075376.177084734212
Trimmed Mean ( 32 / 40 )26.64910714285710.0697817919845776381.891986218222
Trimmed Mean ( 33 / 40 )26.64574074074070.068596594608504388.441159401774
Trimmed Mean ( 34 / 40 )26.64365384615380.067500085942716394.720295152883
Trimmed Mean ( 35 / 40 )26.64240.0664465782046152400.959699052636
Trimmed Mean ( 36 / 40 )26.64083333333330.0652238598309925408.452265817522
Trimmed Mean ( 37 / 40 )26.63956521739130.0640817386558257415.712272734496
Trimmed Mean ( 38 / 40 )26.63727272727270.0630240093486005422.65277951353
Trimmed Mean ( 39 / 40 )26.63571428571430.0619796741410989429.74918237029
Trimmed Mean ( 40 / 40 )26.63550.0612172989628561435.097602332328
Median26.57
Midrange26.66
Midmean - Weighted Average at Xnp26.6131746031746
Midmean - Weighted Average at X(n+1)p26.6548333333333
Midmean - Empirical Distribution Function26.6131746031746
Midmean - Empirical Distribution Function - Averaging26.6548333333333
Midmean - Empirical Distribution Function - Interpolation26.6548333333333
Midmean - Closest Observation26.6131746031746
Midmean - True Basic - Statistics Graphics Toolkit26.6548333333333
Midmean - MS Excel (old versions)26.6315625
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.8301666666667 & 0.124173964404947 & 216.069180002742 \tabularnewline
Geometric Mean & 26.7962066202645 &  &  \tabularnewline
Harmonic Mean & 26.7624926231037 &  &  \tabularnewline
Quadratic Mean & 26.8643392809129 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 26.8316666666667 & 0.123662555519938 & 216.974868050019 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 26.8323333333333 & 0.123377522555348 & 217.481537784130 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 26.8383333333333 & 0.122310410845959 & 219.428036809837 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 26.84 & 0.121946399576814 & 220.096698985308 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 26.8408333333333 & 0.121688263115301 & 220.570436673103 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 26.8413333333333 & 0.121456147250556 & 220.996087402324 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 26.8419166666667 & 0.120644354056595 & 222.487963705911 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 26.8539166666667 & 0.118529582157389 & 226.558772737500 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 26.8531666666667 & 0.116641192697092 & 230.220268206638 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 26.8715 & 0.113836683965436 & 236.053081168097 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 26.8843333333333 & 0.112341499507846 & 239.309012707773 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 26.8903333333333 & 0.111139434298583 & 241.951324505492 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 26.88925 & 0.110966858712379 & 242.317844372758 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 26.8904166666667 & 0.110530006308624 & 243.286122608034 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 26.8891666666667 & 0.107703139012417 & 249.660009106761 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 26.8825 & 0.106668696365493 & 252.018641981795 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 26.874 & 0.104641605235291 & 256.819454743385 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 26.871 & 0.103806502281728 & 258.856616968683 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 26.8678333333333 & 0.102130401028256 & 263.073806259705 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 26.8428333333333 & 0.098465551095638 & 272.611416222729 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 26.8393333333333 & 0.0966661885432009 & 277.649649146336 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 26.843 & 0.0958399108691476 & 280.081646117653 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 26.8410833333333 & 0.0955667742733042 & 280.862083474457 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 26.7890833333333 & 0.087890146278134 & 304.801897229270 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 26.7765833333333 & 0.0842568847674714 & 317.796977745263 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 26.7440833333333 & 0.0795851019792617 & 336.043840721625 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 26.7463333333333 & 0.077794973422597 & 343.805417710501 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 26.7416666666667 & 0.0772151250525531 & 346.32679346781 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 26.7199166666667 & 0.074555592387219 & 358.389167212187 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 26.6974166666667 & 0.069092607832166 & 386.400477624434 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 26.69225 & 0.0679264166155532 & 392.958311801895 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 26.6975833333333 & 0.0667819726753892 & 399.772307761913 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 26.6755833333333 & 0.0642898935901577 & 414.926543562006 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 26.6614166666667 & 0.0621114584837344 & 429.251177118127 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 26.6643333333333 & 0.0611779483409828 & 435.848766694764 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 26.6583333333333 & 0.0586072400826273 & 454.864165173947 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 26.6706666666667 & 0.0560315454034492 & 475.993772340694 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 26.658 & 0.0540135111222507 & 493.543179217955 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 26.6385 & 0.0506254508573485 & 526.187906455618 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 26.6318333333333 & 0.0485756482623578 & 548.254820800216 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 26.8330508474576 & 0.122081191441198 & 219.796764191822 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 26.8344827586207 & 0.120328096249547 & 223.010947526079 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 26.8356140350877 & 0.118547137992523 & 226.370830114687 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 26.8346428571429 & 0.116996816042779 & 229.362163559485 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 26.8331818181818 & 0.115382811507156 & 232.557878142168 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 26.8314814814815 & 0.113648378226744 & 236.092075400752 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 26.8296226415094 & 0.111761918409708 & 240.060505611176 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 26.8275961538462 & 0.109818022396928 & 244.291379213513 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 26.8237254901961 & 0.108037138646394 & 248.282450148835 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 26.8198 & 0.106365956807979 & 252.146464948532 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 26.8134693877551 & 0.104930632616428 & 255.535192337697 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 26.8054166666667 & 0.103521007769958 & 258.936975635256 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 26.7963829787234 & 0.102083852993284 & 262.493843962632 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 26.7870652173913 & 0.100462087897463 & 266.638547714951 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 26.7772222222222 & 0.0986610773517813 & 271.406140506115 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 26.7670454545455 & 0.096986215489936 & 275.988142431673 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 26.7569767441860 & 0.0952008561054636 & 281.058152613088 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 26.7471428571429 & 0.0934198493720701 & 286.311132344209 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 26.7370731707317 & 0.091466273166211 & 292.316197492222 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 26.72675 & 0.0894216252198652 & 298.884637069452 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 26.7178205128205 & 0.0875664720512504 & 305.114730409411 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 26.7086842105263 & 0.08563638800803 & 311.884758708201 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 26.6987837837838 & 0.0834664018234104 & 319.874622608871 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 26.6884722222222 & 0.0809353718588314 & 329.750412079068 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 26.6812857142857 & 0.0791141224154848 & 337.250605829427 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 26.6745588235294 & 0.077463473457396 & 344.350151535615 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 26.6696969696970 & 0.0761662914193456 & 350.150919425271 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 26.664375 & 0.0748354262487052 & 356.306850065698 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 26.6590322580645 & 0.0732976046761755 & 363.709460572996 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 26.6548333333333 & 0.0718325468254293 & 371.069028056475 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 26.6518965517241 & 0.0708493356807075 & 376.177084734212 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 26.6491071428571 & 0.0697817919845776 & 381.891986218222 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 26.6457407407407 & 0.068596594608504 & 388.441159401774 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 26.6436538461538 & 0.067500085942716 & 394.720295152883 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 26.6424 & 0.0664465782046152 & 400.959699052636 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 26.6408333333333 & 0.0652238598309925 & 408.452265817522 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 26.6395652173913 & 0.0640817386558257 & 415.712272734496 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 26.6372727272727 & 0.0630240093486005 & 422.65277951353 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 26.6357142857143 & 0.0619796741410989 & 429.74918237029 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 26.6355 & 0.0612172989628561 & 435.097602332328 \tabularnewline
Median & 26.57 &  &  \tabularnewline
Midrange & 26.66 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.6131746031746 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.6548333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.6131746031746 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.6548333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.6548333333333 &  &  \tabularnewline
Midmean - Closest Observation & 26.6131746031746 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.6548333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.6315625 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52262&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]26.8301666666667[/C][C]0.124173964404947[/C][C]216.069180002742[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26.7962066202645[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]26.7624926231037[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.8643392809129[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]26.8316666666667[/C][C]0.123662555519938[/C][C]216.974868050019[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]26.8323333333333[/C][C]0.123377522555348[/C][C]217.481537784130[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]26.8383333333333[/C][C]0.122310410845959[/C][C]219.428036809837[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]26.84[/C][C]0.121946399576814[/C][C]220.096698985308[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]26.8408333333333[/C][C]0.121688263115301[/C][C]220.570436673103[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]26.8413333333333[/C][C]0.121456147250556[/C][C]220.996087402324[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]26.8419166666667[/C][C]0.120644354056595[/C][C]222.487963705911[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]26.8539166666667[/C][C]0.118529582157389[/C][C]226.558772737500[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]26.8531666666667[/C][C]0.116641192697092[/C][C]230.220268206638[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]26.8715[/C][C]0.113836683965436[/C][C]236.053081168097[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]26.8843333333333[/C][C]0.112341499507846[/C][C]239.309012707773[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]26.8903333333333[/C][C]0.111139434298583[/C][C]241.951324505492[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]26.88925[/C][C]0.110966858712379[/C][C]242.317844372758[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]26.8904166666667[/C][C]0.110530006308624[/C][C]243.286122608034[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]26.8891666666667[/C][C]0.107703139012417[/C][C]249.660009106761[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]26.8825[/C][C]0.106668696365493[/C][C]252.018641981795[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]26.874[/C][C]0.104641605235291[/C][C]256.819454743385[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]26.871[/C][C]0.103806502281728[/C][C]258.856616968683[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]26.8678333333333[/C][C]0.102130401028256[/C][C]263.073806259705[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]26.8428333333333[/C][C]0.098465551095638[/C][C]272.611416222729[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]26.8393333333333[/C][C]0.0966661885432009[/C][C]277.649649146336[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]26.843[/C][C]0.0958399108691476[/C][C]280.081646117653[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]26.8410833333333[/C][C]0.0955667742733042[/C][C]280.862083474457[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]26.7890833333333[/C][C]0.087890146278134[/C][C]304.801897229270[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]26.7765833333333[/C][C]0.0842568847674714[/C][C]317.796977745263[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]26.7440833333333[/C][C]0.0795851019792617[/C][C]336.043840721625[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]26.7463333333333[/C][C]0.077794973422597[/C][C]343.805417710501[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]26.7416666666667[/C][C]0.0772151250525531[/C][C]346.32679346781[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]26.7199166666667[/C][C]0.074555592387219[/C][C]358.389167212187[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]26.6974166666667[/C][C]0.069092607832166[/C][C]386.400477624434[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]26.69225[/C][C]0.0679264166155532[/C][C]392.958311801895[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]26.6975833333333[/C][C]0.0667819726753892[/C][C]399.772307761913[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]26.6755833333333[/C][C]0.0642898935901577[/C][C]414.926543562006[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]26.6614166666667[/C][C]0.0621114584837344[/C][C]429.251177118127[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]26.6643333333333[/C][C]0.0611779483409828[/C][C]435.848766694764[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]26.6583333333333[/C][C]0.0586072400826273[/C][C]454.864165173947[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]26.6706666666667[/C][C]0.0560315454034492[/C][C]475.993772340694[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]26.658[/C][C]0.0540135111222507[/C][C]493.543179217955[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]26.6385[/C][C]0.0506254508573485[/C][C]526.187906455618[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]26.6318333333333[/C][C]0.0485756482623578[/C][C]548.254820800216[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]26.8330508474576[/C][C]0.122081191441198[/C][C]219.796764191822[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]26.8344827586207[/C][C]0.120328096249547[/C][C]223.010947526079[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]26.8356140350877[/C][C]0.118547137992523[/C][C]226.370830114687[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]26.8346428571429[/C][C]0.116996816042779[/C][C]229.362163559485[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]26.8331818181818[/C][C]0.115382811507156[/C][C]232.557878142168[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]26.8314814814815[/C][C]0.113648378226744[/C][C]236.092075400752[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]26.8296226415094[/C][C]0.111761918409708[/C][C]240.060505611176[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]26.8275961538462[/C][C]0.109818022396928[/C][C]244.291379213513[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]26.8237254901961[/C][C]0.108037138646394[/C][C]248.282450148835[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]26.8198[/C][C]0.106365956807979[/C][C]252.146464948532[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]26.8134693877551[/C][C]0.104930632616428[/C][C]255.535192337697[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]26.8054166666667[/C][C]0.103521007769958[/C][C]258.936975635256[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]26.7963829787234[/C][C]0.102083852993284[/C][C]262.493843962632[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]26.7870652173913[/C][C]0.100462087897463[/C][C]266.638547714951[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]26.7772222222222[/C][C]0.0986610773517813[/C][C]271.406140506115[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]26.7670454545455[/C][C]0.096986215489936[/C][C]275.988142431673[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]26.7569767441860[/C][C]0.0952008561054636[/C][C]281.058152613088[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]26.7471428571429[/C][C]0.0934198493720701[/C][C]286.311132344209[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]26.7370731707317[/C][C]0.091466273166211[/C][C]292.316197492222[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]26.72675[/C][C]0.0894216252198652[/C][C]298.884637069452[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]26.7178205128205[/C][C]0.0875664720512504[/C][C]305.114730409411[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]26.7086842105263[/C][C]0.08563638800803[/C][C]311.884758708201[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]26.6987837837838[/C][C]0.0834664018234104[/C][C]319.874622608871[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]26.6884722222222[/C][C]0.0809353718588314[/C][C]329.750412079068[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]26.6812857142857[/C][C]0.0791141224154848[/C][C]337.250605829427[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]26.6745588235294[/C][C]0.077463473457396[/C][C]344.350151535615[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]26.6696969696970[/C][C]0.0761662914193456[/C][C]350.150919425271[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]26.664375[/C][C]0.0748354262487052[/C][C]356.306850065698[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]26.6590322580645[/C][C]0.0732976046761755[/C][C]363.709460572996[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]26.6548333333333[/C][C]0.0718325468254293[/C][C]371.069028056475[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]26.6518965517241[/C][C]0.0708493356807075[/C][C]376.177084734212[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]26.6491071428571[/C][C]0.0697817919845776[/C][C]381.891986218222[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]26.6457407407407[/C][C]0.068596594608504[/C][C]388.441159401774[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]26.6436538461538[/C][C]0.067500085942716[/C][C]394.720295152883[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]26.6424[/C][C]0.0664465782046152[/C][C]400.959699052636[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]26.6408333333333[/C][C]0.0652238598309925[/C][C]408.452265817522[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]26.6395652173913[/C][C]0.0640817386558257[/C][C]415.712272734496[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]26.6372727272727[/C][C]0.0630240093486005[/C][C]422.65277951353[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]26.6357142857143[/C][C]0.0619796741410989[/C][C]429.74918237029[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]26.6355[/C][C]0.0612172989628561[/C][C]435.097602332328[/C][/ROW]
[ROW][C]Median[/C][C]26.57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]26.66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.6131746031746[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.6548333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.6131746031746[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.6548333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.6548333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.6131746031746[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.6548333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.6315625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52262&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 Mean26.83016666666670.124173964404947216.069180002742
Geometric Mean26.7962066202645
Harmonic Mean26.7624926231037
Quadratic Mean26.8643392809129
Winsorized Mean ( 1 / 40 )26.83166666666670.123662555519938216.974868050019
Winsorized Mean ( 2 / 40 )26.83233333333330.123377522555348217.481537784130
Winsorized Mean ( 3 / 40 )26.83833333333330.122310410845959219.428036809837
Winsorized Mean ( 4 / 40 )26.840.121946399576814220.096698985308
Winsorized Mean ( 5 / 40 )26.84083333333330.121688263115301220.570436673103
Winsorized Mean ( 6 / 40 )26.84133333333330.121456147250556220.996087402324
Winsorized Mean ( 7 / 40 )26.84191666666670.120644354056595222.487963705911
Winsorized Mean ( 8 / 40 )26.85391666666670.118529582157389226.558772737500
Winsorized Mean ( 9 / 40 )26.85316666666670.116641192697092230.220268206638
Winsorized Mean ( 10 / 40 )26.87150.113836683965436236.053081168097
Winsorized Mean ( 11 / 40 )26.88433333333330.112341499507846239.309012707773
Winsorized Mean ( 12 / 40 )26.89033333333330.111139434298583241.951324505492
Winsorized Mean ( 13 / 40 )26.889250.110966858712379242.317844372758
Winsorized Mean ( 14 / 40 )26.89041666666670.110530006308624243.286122608034
Winsorized Mean ( 15 / 40 )26.88916666666670.107703139012417249.660009106761
Winsorized Mean ( 16 / 40 )26.88250.106668696365493252.018641981795
Winsorized Mean ( 17 / 40 )26.8740.104641605235291256.819454743385
Winsorized Mean ( 18 / 40 )26.8710.103806502281728258.856616968683
Winsorized Mean ( 19 / 40 )26.86783333333330.102130401028256263.073806259705
Winsorized Mean ( 20 / 40 )26.84283333333330.098465551095638272.611416222729
Winsorized Mean ( 21 / 40 )26.83933333333330.0966661885432009277.649649146336
Winsorized Mean ( 22 / 40 )26.8430.0958399108691476280.081646117653
Winsorized Mean ( 23 / 40 )26.84108333333330.0955667742733042280.862083474457
Winsorized Mean ( 24 / 40 )26.78908333333330.087890146278134304.801897229270
Winsorized Mean ( 25 / 40 )26.77658333333330.0842568847674714317.796977745263
Winsorized Mean ( 26 / 40 )26.74408333333330.0795851019792617336.043840721625
Winsorized Mean ( 27 / 40 )26.74633333333330.077794973422597343.805417710501
Winsorized Mean ( 28 / 40 )26.74166666666670.0772151250525531346.32679346781
Winsorized Mean ( 29 / 40 )26.71991666666670.074555592387219358.389167212187
Winsorized Mean ( 30 / 40 )26.69741666666670.069092607832166386.400477624434
Winsorized Mean ( 31 / 40 )26.692250.0679264166155532392.958311801895
Winsorized Mean ( 32 / 40 )26.69758333333330.0667819726753892399.772307761913
Winsorized Mean ( 33 / 40 )26.67558333333330.0642898935901577414.926543562006
Winsorized Mean ( 34 / 40 )26.66141666666670.0621114584837344429.251177118127
Winsorized Mean ( 35 / 40 )26.66433333333330.0611779483409828435.848766694764
Winsorized Mean ( 36 / 40 )26.65833333333330.0586072400826273454.864165173947
Winsorized Mean ( 37 / 40 )26.67066666666670.0560315454034492475.993772340694
Winsorized Mean ( 38 / 40 )26.6580.0540135111222507493.543179217955
Winsorized Mean ( 39 / 40 )26.63850.0506254508573485526.187906455618
Winsorized Mean ( 40 / 40 )26.63183333333330.0485756482623578548.254820800216
Trimmed Mean ( 1 / 40 )26.83305084745760.122081191441198219.796764191822
Trimmed Mean ( 2 / 40 )26.83448275862070.120328096249547223.010947526079
Trimmed Mean ( 3 / 40 )26.83561403508770.118547137992523226.370830114687
Trimmed Mean ( 4 / 40 )26.83464285714290.116996816042779229.362163559485
Trimmed Mean ( 5 / 40 )26.83318181818180.115382811507156232.557878142168
Trimmed Mean ( 6 / 40 )26.83148148148150.113648378226744236.092075400752
Trimmed Mean ( 7 / 40 )26.82962264150940.111761918409708240.060505611176
Trimmed Mean ( 8 / 40 )26.82759615384620.109818022396928244.291379213513
Trimmed Mean ( 9 / 40 )26.82372549019610.108037138646394248.282450148835
Trimmed Mean ( 10 / 40 )26.81980.106365956807979252.146464948532
Trimmed Mean ( 11 / 40 )26.81346938775510.104930632616428255.535192337697
Trimmed Mean ( 12 / 40 )26.80541666666670.103521007769958258.936975635256
Trimmed Mean ( 13 / 40 )26.79638297872340.102083852993284262.493843962632
Trimmed Mean ( 14 / 40 )26.78706521739130.100462087897463266.638547714951
Trimmed Mean ( 15 / 40 )26.77722222222220.0986610773517813271.406140506115
Trimmed Mean ( 16 / 40 )26.76704545454550.096986215489936275.988142431673
Trimmed Mean ( 17 / 40 )26.75697674418600.0952008561054636281.058152613088
Trimmed Mean ( 18 / 40 )26.74714285714290.0934198493720701286.311132344209
Trimmed Mean ( 19 / 40 )26.73707317073170.091466273166211292.316197492222
Trimmed Mean ( 20 / 40 )26.726750.0894216252198652298.884637069452
Trimmed Mean ( 21 / 40 )26.71782051282050.0875664720512504305.114730409411
Trimmed Mean ( 22 / 40 )26.70868421052630.08563638800803311.884758708201
Trimmed Mean ( 23 / 40 )26.69878378378380.0834664018234104319.874622608871
Trimmed Mean ( 24 / 40 )26.68847222222220.0809353718588314329.750412079068
Trimmed Mean ( 25 / 40 )26.68128571428570.0791141224154848337.250605829427
Trimmed Mean ( 26 / 40 )26.67455882352940.077463473457396344.350151535615
Trimmed Mean ( 27 / 40 )26.66969696969700.0761662914193456350.150919425271
Trimmed Mean ( 28 / 40 )26.6643750.0748354262487052356.306850065698
Trimmed Mean ( 29 / 40 )26.65903225806450.0732976046761755363.709460572996
Trimmed Mean ( 30 / 40 )26.65483333333330.0718325468254293371.069028056475
Trimmed Mean ( 31 / 40 )26.65189655172410.0708493356807075376.177084734212
Trimmed Mean ( 32 / 40 )26.64910714285710.0697817919845776381.891986218222
Trimmed Mean ( 33 / 40 )26.64574074074070.068596594608504388.441159401774
Trimmed Mean ( 34 / 40 )26.64365384615380.067500085942716394.720295152883
Trimmed Mean ( 35 / 40 )26.64240.0664465782046152400.959699052636
Trimmed Mean ( 36 / 40 )26.64083333333330.0652238598309925408.452265817522
Trimmed Mean ( 37 / 40 )26.63956521739130.0640817386558257415.712272734496
Trimmed Mean ( 38 / 40 )26.63727272727270.0630240093486005422.65277951353
Trimmed Mean ( 39 / 40 )26.63571428571430.0619796741410989429.74918237029
Trimmed Mean ( 40 / 40 )26.63550.0612172989628561435.097602332328
Median26.57
Midrange26.66
Midmean - Weighted Average at Xnp26.6131746031746
Midmean - Weighted Average at X(n+1)p26.6548333333333
Midmean - Empirical Distribution Function26.6131746031746
Midmean - Empirical Distribution Function - Averaging26.6548333333333
Midmean - Empirical Distribution Function - Interpolation26.6548333333333
Midmean - Closest Observation26.6131746031746
Midmean - True Basic - Statistics Graphics Toolkit26.6548333333333
Midmean - MS Excel (old versions)26.6315625
Number of observations120



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')