Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 12:37:37 +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/2017/Mar/14/t14894951071pmn4rsmf6ecp64.htm/, Retrieved Wed, 15 May 2024 00:46:49 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 00:46:49 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
90,36
90,67
91,21
91,35
91,62
91,28
91,17
91,13
91,55
91,62
91,73
91,91
92,5
92,93
92,77
93,42
93,82
94,02
94,13
93,7
93,84
94,22
95,03
95,03
95,25
96,11
96,16
96,1
96,52
96,35
96,35
96,66
96,86
97,84
98,04
98,06
98,79
99,38
99,75
100,4
100,97
101,16
100,42
99,88
99,8
99,78
99,78
99,89
100,38
100,1
100,02
101,15
100,02
99,99
100,14
98,93
98,52
98,42
98,78
99,04
99,53
99,97
99,95
101,68
101,29
101,45
100,98
100,64
100,6
101,59
101,15
101,03




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.03694444444440.423430021068573229.168787323017
Geometric Mean96.9705791822235
Harmonic Mean96.9034754619802
Quadratic Mean97.1025148432773
Winsorized Mean ( 1 / 24 )97.040.422303143756848229.787538725673
Winsorized Mean ( 2 / 24 )97.04888888888890.419091934907324231.569450054795
Winsorized Mean ( 3 / 24 )97.04388888888890.417790950579794232.278580362297
Winsorized Mean ( 4 / 24 )97.03888888888890.416331440526317233.080856843803
Winsorized Mean ( 5 / 24 )97.04305555555560.415280305758527233.680851728093
Winsorized Mean ( 6 / 24 )97.04888888888890.414144930308577234.335571406315
Winsorized Mean ( 7 / 24 )97.05666666666670.408803647898611237.416341966543
Winsorized Mean ( 8 / 24 )97.05888888888890.406575528325308238.722899257307
Winsorized Mean ( 9 / 24 )97.05763888888890.406405889462313238.819469415906
Winsorized Mean ( 10 / 24 )97.02708333333330.397489600729118244.099677464155
Winsorized Mean ( 11 / 24 )97.04847222222220.391585730310983247.834547354803
Winsorized Mean ( 12 / 24 )97.11680555555560.370043500085797262.44699753688
Winsorized Mean ( 13 / 24 )97.16194444444440.361128666661264269.050766151394
Winsorized Mean ( 14 / 24 )97.18916666666670.35534630940642273.505490542491
Winsorized Mean ( 15 / 24 )97.241250.332211665461967292.708715886837
Winsorized Mean ( 16 / 24 )97.29458333333330.321171986837439302.936081977097
Winsorized Mean ( 17 / 24 )97.30402777777780.314416496332446309.474944580815
Winsorized Mean ( 18 / 24 )97.30902777777780.313636862256789310.260175024026
Winsorized Mean ( 19 / 24 )97.34861111111110.305325341857023318.835673839014
Winsorized Mean ( 20 / 24 )97.37361111111110.299975501448551324.605211561957
Winsorized Mean ( 21 / 24 )97.39402777777780.295278287065429329.83809526163
Winsorized Mean ( 22 / 24 )97.62319444444440.256592866835751380.459502434004
Winsorized Mean ( 23 / 24 )97.620.256195683964432381.036864046284
Winsorized Mean ( 24 / 24 )97.66666666666670.242517927640241402.719368489528
Trimmed Mean ( 1 / 24 )97.0660.419589437505584231.335661300359
Trimmed Mean ( 2 / 24 )97.09352941176470.416125823304868233.327335084972
Trimmed Mean ( 3 / 24 )97.11787878787880.413732372713134234.735991653272
Trimmed Mean ( 4 / 24 )97.1456250.411125468130636236.29191701919
Trimmed Mean ( 5 / 24 )97.17661290322580.408172394362011238.077376729792
Trimmed Mean ( 6 / 24 )97.20866666666670.404592105864734240.26337948167
Trimmed Mean ( 7 / 24 )97.2417241379310.400226050609995242.967003246596
Trimmed Mean ( 8 / 24 )97.27571428571430.395898850483897245.708503994939
Trimmed Mean ( 9 / 24 )97.31185185185190.390741565404292249.044024152295
Trimmed Mean ( 10 / 24 )97.35096153846150.384027071736093253.500257412483
Trimmed Mean ( 11 / 24 )97.39760.377200597311623258.211680188659
Trimmed Mean ( 12 / 24 )97.44520833333330.369557909835423263.680483463956
Trimmed Mean ( 13 / 24 )97.48804347826090.364300616371187267.603289967893
Trimmed Mean ( 14 / 24 )97.52909090909090.359046749766883271.633404208263
Trimmed Mean ( 15 / 24 )97.57071428571430.352981558423888276.418730546097
Trimmed Mean ( 16 / 24 )97.610250.349598760394299279.206510600635
Trimmed Mean ( 17 / 24 )97.64763157894740.346820640658401281.550807914933
Trimmed Mean ( 18 / 24 )97.68805555555560.343629511511538284.283078964467
Trimmed Mean ( 19 / 24 )97.73264705882350.338378831048689288.826126492413
Trimmed Mean ( 20 / 24 )97.7781250.33227540240643294.268321674924
Trimmed Mean ( 21 / 24 )97.82666666666670.324019061924482301.916393701142
Trimmed Mean ( 22 / 24 )97.87964285714290.312323381684413313.391979586226
Trimmed Mean ( 23 / 24 )97.91192307692310.307735160477452318.169438048654
Trimmed Mean ( 24 / 24 )97.950.298977726861752327.616378076526
Median98.24
Midrange96.02
Midmean - Weighted Average at Xnp97.6476315789474
Midmean - Weighted Average at X(n+1)p97.7510810810811
Midmean - Empirical Distribution Function97.6476315789474
Midmean - Empirical Distribution Function - Averaging97.7510810810811
Midmean - Empirical Distribution Function - Interpolation97.7510810810811
Midmean - Closest Observation97.6476315789474
Midmean - True Basic - Statistics Graphics Toolkit97.7510810810811
Midmean - MS Excel (old versions)97.6476315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.0369444444444 & 0.423430021068573 & 229.168787323017 \tabularnewline
Geometric Mean & 96.9705791822235 &  &  \tabularnewline
Harmonic Mean & 96.9034754619802 &  &  \tabularnewline
Quadratic Mean & 97.1025148432773 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 97.04 & 0.422303143756848 & 229.787538725673 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 97.0488888888889 & 0.419091934907324 & 231.569450054795 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 97.0438888888889 & 0.417790950579794 & 232.278580362297 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.0388888888889 & 0.416331440526317 & 233.080856843803 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.0430555555556 & 0.415280305758527 & 233.680851728093 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.0488888888889 & 0.414144930308577 & 234.335571406315 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.0566666666667 & 0.408803647898611 & 237.416341966543 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.0588888888889 & 0.406575528325308 & 238.722899257307 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.0576388888889 & 0.406405889462313 & 238.819469415906 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.0270833333333 & 0.397489600729118 & 244.099677464155 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.0484722222222 & 0.391585730310983 & 247.834547354803 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.1168055555556 & 0.370043500085797 & 262.44699753688 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.1619444444444 & 0.361128666661264 & 269.050766151394 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.1891666666667 & 0.35534630940642 & 273.505490542491 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.24125 & 0.332211665461967 & 292.708715886837 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.2945833333333 & 0.321171986837439 & 302.936081977097 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.3040277777778 & 0.314416496332446 & 309.474944580815 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.3090277777778 & 0.313636862256789 & 310.260175024026 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.3486111111111 & 0.305325341857023 & 318.835673839014 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.3736111111111 & 0.299975501448551 & 324.605211561957 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.3940277777778 & 0.295278287065429 & 329.83809526163 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.6231944444444 & 0.256592866835751 & 380.459502434004 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.62 & 0.256195683964432 & 381.036864046284 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.6666666666667 & 0.242517927640241 & 402.719368489528 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.066 & 0.419589437505584 & 231.335661300359 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.0935294117647 & 0.416125823304868 & 233.327335084972 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.1178787878788 & 0.413732372713134 & 234.735991653272 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.145625 & 0.411125468130636 & 236.29191701919 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.1766129032258 & 0.408172394362011 & 238.077376729792 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.2086666666667 & 0.404592105864734 & 240.26337948167 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.241724137931 & 0.400226050609995 & 242.967003246596 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.2757142857143 & 0.395898850483897 & 245.708503994939 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.3118518518519 & 0.390741565404292 & 249.044024152295 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.3509615384615 & 0.384027071736093 & 253.500257412483 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.3976 & 0.377200597311623 & 258.211680188659 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.4452083333333 & 0.369557909835423 & 263.680483463956 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.4880434782609 & 0.364300616371187 & 267.603289967893 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.5290909090909 & 0.359046749766883 & 271.633404208263 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.5707142857143 & 0.352981558423888 & 276.418730546097 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.61025 & 0.349598760394299 & 279.206510600635 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.6476315789474 & 0.346820640658401 & 281.550807914933 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.6880555555556 & 0.343629511511538 & 284.283078964467 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.7326470588235 & 0.338378831048689 & 288.826126492413 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.778125 & 0.33227540240643 & 294.268321674924 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.8266666666667 & 0.324019061924482 & 301.916393701142 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.8796428571429 & 0.312323381684413 & 313.391979586226 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.9119230769231 & 0.307735160477452 & 318.169438048654 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.95 & 0.298977726861752 & 327.616378076526 \tabularnewline
Median & 98.24 &  &  \tabularnewline
Midrange & 96.02 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.6476315789474 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.7510810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.6476315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.7510810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.7510810810811 &  &  \tabularnewline
Midmean - Closest Observation & 97.6476315789474 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.7510810810811 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.6476315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]97.0369444444444[/C][C]0.423430021068573[/C][C]229.168787323017[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.9705791822235[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.9034754619802[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.1025148432773[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]97.04[/C][C]0.422303143756848[/C][C]229.787538725673[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]97.0488888888889[/C][C]0.419091934907324[/C][C]231.569450054795[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]97.0438888888889[/C][C]0.417790950579794[/C][C]232.278580362297[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.0388888888889[/C][C]0.416331440526317[/C][C]233.080856843803[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.0430555555556[/C][C]0.415280305758527[/C][C]233.680851728093[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.0488888888889[/C][C]0.414144930308577[/C][C]234.335571406315[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.0566666666667[/C][C]0.408803647898611[/C][C]237.416341966543[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.0588888888889[/C][C]0.406575528325308[/C][C]238.722899257307[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.0576388888889[/C][C]0.406405889462313[/C][C]238.819469415906[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.0270833333333[/C][C]0.397489600729118[/C][C]244.099677464155[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.0484722222222[/C][C]0.391585730310983[/C][C]247.834547354803[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.1168055555556[/C][C]0.370043500085797[/C][C]262.44699753688[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.1619444444444[/C][C]0.361128666661264[/C][C]269.050766151394[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.1891666666667[/C][C]0.35534630940642[/C][C]273.505490542491[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.24125[/C][C]0.332211665461967[/C][C]292.708715886837[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.2945833333333[/C][C]0.321171986837439[/C][C]302.936081977097[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.3040277777778[/C][C]0.314416496332446[/C][C]309.474944580815[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.3090277777778[/C][C]0.313636862256789[/C][C]310.260175024026[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.3486111111111[/C][C]0.305325341857023[/C][C]318.835673839014[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.3736111111111[/C][C]0.299975501448551[/C][C]324.605211561957[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.3940277777778[/C][C]0.295278287065429[/C][C]329.83809526163[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.6231944444444[/C][C]0.256592866835751[/C][C]380.459502434004[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.62[/C][C]0.256195683964432[/C][C]381.036864046284[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.6666666666667[/C][C]0.242517927640241[/C][C]402.719368489528[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.066[/C][C]0.419589437505584[/C][C]231.335661300359[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.0935294117647[/C][C]0.416125823304868[/C][C]233.327335084972[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.1178787878788[/C][C]0.413732372713134[/C][C]234.735991653272[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.145625[/C][C]0.411125468130636[/C][C]236.29191701919[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.1766129032258[/C][C]0.408172394362011[/C][C]238.077376729792[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.2086666666667[/C][C]0.404592105864734[/C][C]240.26337948167[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.241724137931[/C][C]0.400226050609995[/C][C]242.967003246596[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.2757142857143[/C][C]0.395898850483897[/C][C]245.708503994939[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.3118518518519[/C][C]0.390741565404292[/C][C]249.044024152295[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.3509615384615[/C][C]0.384027071736093[/C][C]253.500257412483[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.3976[/C][C]0.377200597311623[/C][C]258.211680188659[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.4452083333333[/C][C]0.369557909835423[/C][C]263.680483463956[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.4880434782609[/C][C]0.364300616371187[/C][C]267.603289967893[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.5290909090909[/C][C]0.359046749766883[/C][C]271.633404208263[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.5707142857143[/C][C]0.352981558423888[/C][C]276.418730546097[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.61025[/C][C]0.349598760394299[/C][C]279.206510600635[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.6476315789474[/C][C]0.346820640658401[/C][C]281.550807914933[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.6880555555556[/C][C]0.343629511511538[/C][C]284.283078964467[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.7326470588235[/C][C]0.338378831048689[/C][C]288.826126492413[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.778125[/C][C]0.33227540240643[/C][C]294.268321674924[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.8266666666667[/C][C]0.324019061924482[/C][C]301.916393701142[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.8796428571429[/C][C]0.312323381684413[/C][C]313.391979586226[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.9119230769231[/C][C]0.307735160477452[/C][C]318.169438048654[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.95[/C][C]0.298977726861752[/C][C]327.616378076526[/C][/ROW]
[ROW][C]Median[/C][C]98.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.6476315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.7510810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.6476315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.7510810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.7510810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.6476315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.7510810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.6476315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean97.03694444444440.423430021068573229.168787323017
Geometric Mean96.9705791822235
Harmonic Mean96.9034754619802
Quadratic Mean97.1025148432773
Winsorized Mean ( 1 / 24 )97.040.422303143756848229.787538725673
Winsorized Mean ( 2 / 24 )97.04888888888890.419091934907324231.569450054795
Winsorized Mean ( 3 / 24 )97.04388888888890.417790950579794232.278580362297
Winsorized Mean ( 4 / 24 )97.03888888888890.416331440526317233.080856843803
Winsorized Mean ( 5 / 24 )97.04305555555560.415280305758527233.680851728093
Winsorized Mean ( 6 / 24 )97.04888888888890.414144930308577234.335571406315
Winsorized Mean ( 7 / 24 )97.05666666666670.408803647898611237.416341966543
Winsorized Mean ( 8 / 24 )97.05888888888890.406575528325308238.722899257307
Winsorized Mean ( 9 / 24 )97.05763888888890.406405889462313238.819469415906
Winsorized Mean ( 10 / 24 )97.02708333333330.397489600729118244.099677464155
Winsorized Mean ( 11 / 24 )97.04847222222220.391585730310983247.834547354803
Winsorized Mean ( 12 / 24 )97.11680555555560.370043500085797262.44699753688
Winsorized Mean ( 13 / 24 )97.16194444444440.361128666661264269.050766151394
Winsorized Mean ( 14 / 24 )97.18916666666670.35534630940642273.505490542491
Winsorized Mean ( 15 / 24 )97.241250.332211665461967292.708715886837
Winsorized Mean ( 16 / 24 )97.29458333333330.321171986837439302.936081977097
Winsorized Mean ( 17 / 24 )97.30402777777780.314416496332446309.474944580815
Winsorized Mean ( 18 / 24 )97.30902777777780.313636862256789310.260175024026
Winsorized Mean ( 19 / 24 )97.34861111111110.305325341857023318.835673839014
Winsorized Mean ( 20 / 24 )97.37361111111110.299975501448551324.605211561957
Winsorized Mean ( 21 / 24 )97.39402777777780.295278287065429329.83809526163
Winsorized Mean ( 22 / 24 )97.62319444444440.256592866835751380.459502434004
Winsorized Mean ( 23 / 24 )97.620.256195683964432381.036864046284
Winsorized Mean ( 24 / 24 )97.66666666666670.242517927640241402.719368489528
Trimmed Mean ( 1 / 24 )97.0660.419589437505584231.335661300359
Trimmed Mean ( 2 / 24 )97.09352941176470.416125823304868233.327335084972
Trimmed Mean ( 3 / 24 )97.11787878787880.413732372713134234.735991653272
Trimmed Mean ( 4 / 24 )97.1456250.411125468130636236.29191701919
Trimmed Mean ( 5 / 24 )97.17661290322580.408172394362011238.077376729792
Trimmed Mean ( 6 / 24 )97.20866666666670.404592105864734240.26337948167
Trimmed Mean ( 7 / 24 )97.2417241379310.400226050609995242.967003246596
Trimmed Mean ( 8 / 24 )97.27571428571430.395898850483897245.708503994939
Trimmed Mean ( 9 / 24 )97.31185185185190.390741565404292249.044024152295
Trimmed Mean ( 10 / 24 )97.35096153846150.384027071736093253.500257412483
Trimmed Mean ( 11 / 24 )97.39760.377200597311623258.211680188659
Trimmed Mean ( 12 / 24 )97.44520833333330.369557909835423263.680483463956
Trimmed Mean ( 13 / 24 )97.48804347826090.364300616371187267.603289967893
Trimmed Mean ( 14 / 24 )97.52909090909090.359046749766883271.633404208263
Trimmed Mean ( 15 / 24 )97.57071428571430.352981558423888276.418730546097
Trimmed Mean ( 16 / 24 )97.610250.349598760394299279.206510600635
Trimmed Mean ( 17 / 24 )97.64763157894740.346820640658401281.550807914933
Trimmed Mean ( 18 / 24 )97.68805555555560.343629511511538284.283078964467
Trimmed Mean ( 19 / 24 )97.73264705882350.338378831048689288.826126492413
Trimmed Mean ( 20 / 24 )97.7781250.33227540240643294.268321674924
Trimmed Mean ( 21 / 24 )97.82666666666670.324019061924482301.916393701142
Trimmed Mean ( 22 / 24 )97.87964285714290.312323381684413313.391979586226
Trimmed Mean ( 23 / 24 )97.91192307692310.307735160477452318.169438048654
Trimmed Mean ( 24 / 24 )97.950.298977726861752327.616378076526
Median98.24
Midrange96.02
Midmean - Weighted Average at Xnp97.6476315789474
Midmean - Weighted Average at X(n+1)p97.7510810810811
Midmean - Empirical Distribution Function97.6476315789474
Midmean - Empirical Distribution Function - Averaging97.7510810810811
Midmean - Empirical Distribution Function - Interpolation97.7510810810811
Midmean - Closest Observation97.6476315789474
Midmean - True Basic - Statistics Graphics Toolkit97.7510810810811
Midmean - MS Excel (old versions)97.6476315789474
Number of observations72



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