Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 05:19:22 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331115583ybita8h5yt1k2s3.htm/, Retrieved Mon, 29 Apr 2024 05:17:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163581, Retrieved Mon, 29 Apr 2024 05:17:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 10:19:22] [57781dd4fd8fc2f3d4652fc8b989af11] [Current]
Feedback Forum

Post a new message
Dataseries X:
-6
-3
-2
-5
-11
-11
-11
-10
-14
-8
-9
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163581&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163581&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163581&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-7.930555555555560.822779743202927-9.63873457151898
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.5336761547588
Winsorized Mean ( 1 / 24 )-7.916666666666670.818829176725694-9.66827623109812
Winsorized Mean ( 2 / 24 )-7.916666666666670.818829176725694-9.66827623109812
Winsorized Mean ( 3 / 24 )-7.8750.789935096678206-9.96917345882661
Winsorized Mean ( 4 / 24 )-7.8750.789935096678206-9.96917345882661
Winsorized Mean ( 5 / 24 )-7.736111111111110.756555351462216-10.2254396802023
Winsorized Mean ( 6 / 24 )-7.736111111111110.724863878958391-10.6725018802533
Winsorized Mean ( 7 / 24 )-7.736111111111110.690023092635832-11.2113800156453
Winsorized Mean ( 8 / 24 )-7.6250.667381512286711-11.4252490661208
Winsorized Mean ( 9 / 24 )-7.6250.667381512286711-11.4252490661208
Winsorized Mean ( 10 / 24 )-7.347222222222220.615450431835296-11.9379593256804
Winsorized Mean ( 11 / 24 )-7.347222222222220.615450431835296-11.9379593256804
Winsorized Mean ( 12 / 24 )-7.513888888888890.592398725705376-12.6838370220024
Winsorized Mean ( 13 / 24 )-7.333333333333330.561199810154154-13.0672412938254
Winsorized Mean ( 14 / 24 )-7.138888888888890.529750862530623-13.4759363199266
Winsorized Mean ( 15 / 24 )-7.138888888888890.529750862530623-13.4759363199266
Winsorized Mean ( 16 / 24 )-7.138888888888890.529750862530623-13.4759363199266
Winsorized Mean ( 17 / 24 )-6.902777777777780.494159837027844-13.9687146962306
Winsorized Mean ( 18 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 19 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 20 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 21 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 22 / 24 )-6.958333333333330.416989311699937-16.6870783928882
Winsorized Mean ( 23 / 24 )-6.958333333333330.416989311699937-16.6870783928882
Winsorized Mean ( 24 / 24 )-6.958333333333330.416989311699937-16.6870783928882
Trimmed Mean ( 1 / 24 )-7.828571428571430.797244589336462-9.81953535123651
Trimmed Mean ( 2 / 24 )-7.735294117647060.771421514627631-10.0273248424772
Trimmed Mean ( 3 / 24 )-7.636363636363640.740325753171868-10.3148696417033
Trimmed Mean ( 4 / 24 )-7.5468750.716490041738693-10.5331191787204
Trimmed Mean ( 5 / 24 )-7.451612903225810.687455558625084-10.8394103585824
Trimmed Mean ( 6 / 24 )-7.383333333333330.663449156625808-11.1287101047558
Trimmed Mean ( 7 / 24 )-7.310344827586210.643364801435695-11.3626745063965
Trimmed Mean ( 8 / 24 )-7.232142857142860.627813703563556-11.5195683306883
Trimmed Mean ( 9 / 24 )-7.166666666666670.614152902428334-11.669189607881
Trimmed Mean ( 10 / 24 )-7.096153846153850.596786022035533-11.8906167104084
Trimmed Mean ( 11 / 24 )-7.060.58721758300984-12.022800754387
Trimmed Mean ( 12 / 24 )-7.020833333333330.574648816078421-12.2176068877086
Trimmed Mean ( 13 / 24 )-6.956521739130430.562908700038354-12.3581705854901
Trimmed Mean ( 14 / 24 )-6.909090909090910.554453602069616-12.4610803921216
Trimmed Mean ( 15 / 24 )-6.880952380952380.549735847191043-12.5168340687835
Trimmed Mean ( 16 / 24 )-6.850.542489513073637-12.6269721993136
Trimmed Mean ( 17 / 24 )-6.815789473684210.531852105077648-12.8151969478228
Trimmed Mean ( 18 / 24 )-6.805555555555560.525265532916968-12.9564099090266
Trimmed Mean ( 19 / 24 )-6.823529411764710.523035477703332-13.0460163844469
Trimmed Mean ( 20 / 24 )-6.843750.518040225661315-13.2108466891031
Trimmed Mean ( 21 / 24 )-6.866666666666670.509074737266156-13.4885237156772
Trimmed Mean ( 22 / 24 )-6.892857142857140.494250771006953-13.9460726157576
Trimmed Mean ( 23 / 24 )-6.884615384615390.484615384615385-14.2063492063492
Trimmed Mean ( 24 / 24 )-6.8750.467465026204782-14.7069825860903
Median-7
Midrange-11.5
Midmean - Weighted Average at Xnp-6.25581395348837
Midmean - Weighted Average at X(n+1)p-6.11904761904762
Midmean - Empirical Distribution Function-6.25581395348837
Midmean - Empirical Distribution Function - Averaging-6.11904761904762
Midmean - Empirical Distribution Function - Interpolation-6.11904761904762
Midmean - Closest Observation-6.25581395348837
Midmean - True Basic - Statistics Graphics Toolkit-6.11904761904762
Midmean - MS Excel (old versions)-6.25581395348837
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -7.93055555555556 & 0.822779743202927 & -9.63873457151898 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 10.5336761547588 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -7.91666666666667 & 0.818829176725694 & -9.66827623109812 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -7.91666666666667 & 0.818829176725694 & -9.66827623109812 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -7.875 & 0.789935096678206 & -9.96917345882661 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -7.875 & 0.789935096678206 & -9.96917345882661 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -7.73611111111111 & 0.756555351462216 & -10.2254396802023 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -7.73611111111111 & 0.724863878958391 & -10.6725018802533 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -7.73611111111111 & 0.690023092635832 & -11.2113800156453 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -7.625 & 0.667381512286711 & -11.4252490661208 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -7.625 & 0.667381512286711 & -11.4252490661208 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -7.34722222222222 & 0.615450431835296 & -11.9379593256804 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -7.34722222222222 & 0.615450431835296 & -11.9379593256804 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -7.51388888888889 & 0.592398725705376 & -12.6838370220024 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -7.33333333333333 & 0.561199810154154 & -13.0672412938254 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -7.13888888888889 & 0.529750862530623 & -13.4759363199266 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -7.13888888888889 & 0.529750862530623 & -13.4759363199266 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -7.13888888888889 & 0.529750862530623 & -13.4759363199266 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -6.90277777777778 & 0.494159837027844 & -13.9687146962306 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -6.65277777777778 & 0.459280805672737 & -14.485207514895 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -6.65277777777778 & 0.459280805672737 & -14.485207514895 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -6.65277777777778 & 0.459280805672737 & -14.485207514895 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -6.65277777777778 & 0.459280805672737 & -14.485207514895 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -6.95833333333333 & 0.416989311699937 & -16.6870783928882 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -6.95833333333333 & 0.416989311699937 & -16.6870783928882 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -6.95833333333333 & 0.416989311699937 & -16.6870783928882 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -7.82857142857143 & 0.797244589336462 & -9.81953535123651 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -7.73529411764706 & 0.771421514627631 & -10.0273248424772 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -7.63636363636364 & 0.740325753171868 & -10.3148696417033 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -7.546875 & 0.716490041738693 & -10.5331191787204 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -7.45161290322581 & 0.687455558625084 & -10.8394103585824 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -7.38333333333333 & 0.663449156625808 & -11.1287101047558 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -7.31034482758621 & 0.643364801435695 & -11.3626745063965 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -7.23214285714286 & 0.627813703563556 & -11.5195683306883 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -7.16666666666667 & 0.614152902428334 & -11.669189607881 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -7.09615384615385 & 0.596786022035533 & -11.8906167104084 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -7.06 & 0.58721758300984 & -12.022800754387 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -7.02083333333333 & 0.574648816078421 & -12.2176068877086 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -6.95652173913043 & 0.562908700038354 & -12.3581705854901 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -6.90909090909091 & 0.554453602069616 & -12.4610803921216 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -6.88095238095238 & 0.549735847191043 & -12.5168340687835 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -6.85 & 0.542489513073637 & -12.6269721993136 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -6.81578947368421 & 0.531852105077648 & -12.8151969478228 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -6.80555555555556 & 0.525265532916968 & -12.9564099090266 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -6.82352941176471 & 0.523035477703332 & -13.0460163844469 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -6.84375 & 0.518040225661315 & -13.2108466891031 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -6.86666666666667 & 0.509074737266156 & -13.4885237156772 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -6.89285714285714 & 0.494250771006953 & -13.9460726157576 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -6.88461538461539 & 0.484615384615385 & -14.2063492063492 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -6.875 & 0.467465026204782 & -14.7069825860903 \tabularnewline
Median & -7 &  &  \tabularnewline
Midrange & -11.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -6.25581395348837 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -6.11904761904762 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -6.25581395348837 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -6.11904761904762 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -6.11904761904762 &  &  \tabularnewline
Midmean - Closest Observation & -6.25581395348837 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -6.11904761904762 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -6.25581395348837 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163581&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]-7.93055555555556[/C][C]0.822779743202927[/C][C]-9.63873457151898[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.5336761547588[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-7.91666666666667[/C][C]0.818829176725694[/C][C]-9.66827623109812[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-7.91666666666667[/C][C]0.818829176725694[/C][C]-9.66827623109812[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-7.875[/C][C]0.789935096678206[/C][C]-9.96917345882661[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-7.875[/C][C]0.789935096678206[/C][C]-9.96917345882661[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-7.73611111111111[/C][C]0.756555351462216[/C][C]-10.2254396802023[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-7.73611111111111[/C][C]0.724863878958391[/C][C]-10.6725018802533[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-7.73611111111111[/C][C]0.690023092635832[/C][C]-11.2113800156453[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-7.625[/C][C]0.667381512286711[/C][C]-11.4252490661208[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-7.625[/C][C]0.667381512286711[/C][C]-11.4252490661208[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-7.34722222222222[/C][C]0.615450431835296[/C][C]-11.9379593256804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-7.34722222222222[/C][C]0.615450431835296[/C][C]-11.9379593256804[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-7.51388888888889[/C][C]0.592398725705376[/C][C]-12.6838370220024[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-7.33333333333333[/C][C]0.561199810154154[/C][C]-13.0672412938254[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-7.13888888888889[/C][C]0.529750862530623[/C][C]-13.4759363199266[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-7.13888888888889[/C][C]0.529750862530623[/C][C]-13.4759363199266[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-7.13888888888889[/C][C]0.529750862530623[/C][C]-13.4759363199266[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-6.90277777777778[/C][C]0.494159837027844[/C][C]-13.9687146962306[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-6.65277777777778[/C][C]0.459280805672737[/C][C]-14.485207514895[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-6.65277777777778[/C][C]0.459280805672737[/C][C]-14.485207514895[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-6.65277777777778[/C][C]0.459280805672737[/C][C]-14.485207514895[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-6.65277777777778[/C][C]0.459280805672737[/C][C]-14.485207514895[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-6.95833333333333[/C][C]0.416989311699937[/C][C]-16.6870783928882[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-6.95833333333333[/C][C]0.416989311699937[/C][C]-16.6870783928882[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-6.95833333333333[/C][C]0.416989311699937[/C][C]-16.6870783928882[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-7.82857142857143[/C][C]0.797244589336462[/C][C]-9.81953535123651[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-7.73529411764706[/C][C]0.771421514627631[/C][C]-10.0273248424772[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-7.63636363636364[/C][C]0.740325753171868[/C][C]-10.3148696417033[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-7.546875[/C][C]0.716490041738693[/C][C]-10.5331191787204[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-7.45161290322581[/C][C]0.687455558625084[/C][C]-10.8394103585824[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-7.38333333333333[/C][C]0.663449156625808[/C][C]-11.1287101047558[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-7.31034482758621[/C][C]0.643364801435695[/C][C]-11.3626745063965[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-7.23214285714286[/C][C]0.627813703563556[/C][C]-11.5195683306883[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-7.16666666666667[/C][C]0.614152902428334[/C][C]-11.669189607881[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-7.09615384615385[/C][C]0.596786022035533[/C][C]-11.8906167104084[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-7.06[/C][C]0.58721758300984[/C][C]-12.022800754387[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-7.02083333333333[/C][C]0.574648816078421[/C][C]-12.2176068877086[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-6.95652173913043[/C][C]0.562908700038354[/C][C]-12.3581705854901[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-6.90909090909091[/C][C]0.554453602069616[/C][C]-12.4610803921216[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-6.88095238095238[/C][C]0.549735847191043[/C][C]-12.5168340687835[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-6.85[/C][C]0.542489513073637[/C][C]-12.6269721993136[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-6.81578947368421[/C][C]0.531852105077648[/C][C]-12.8151969478228[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-6.80555555555556[/C][C]0.525265532916968[/C][C]-12.9564099090266[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-6.82352941176471[/C][C]0.523035477703332[/C][C]-13.0460163844469[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-6.84375[/C][C]0.518040225661315[/C][C]-13.2108466891031[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-6.86666666666667[/C][C]0.509074737266156[/C][C]-13.4885237156772[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-6.89285714285714[/C][C]0.494250771006953[/C][C]-13.9460726157576[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-6.88461538461539[/C][C]0.484615384615385[/C][C]-14.2063492063492[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-6.875[/C][C]0.467465026204782[/C][C]-14.7069825860903[/C][/ROW]
[ROW][C]Median[/C][C]-7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-11.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-6.25581395348837[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-6.11904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-6.25581395348837[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-6.11904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-6.11904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-6.25581395348837[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-6.11904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-6.25581395348837[/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=163581&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163581&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 Mean-7.930555555555560.822779743202927-9.63873457151898
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.5336761547588
Winsorized Mean ( 1 / 24 )-7.916666666666670.818829176725694-9.66827623109812
Winsorized Mean ( 2 / 24 )-7.916666666666670.818829176725694-9.66827623109812
Winsorized Mean ( 3 / 24 )-7.8750.789935096678206-9.96917345882661
Winsorized Mean ( 4 / 24 )-7.8750.789935096678206-9.96917345882661
Winsorized Mean ( 5 / 24 )-7.736111111111110.756555351462216-10.2254396802023
Winsorized Mean ( 6 / 24 )-7.736111111111110.724863878958391-10.6725018802533
Winsorized Mean ( 7 / 24 )-7.736111111111110.690023092635832-11.2113800156453
Winsorized Mean ( 8 / 24 )-7.6250.667381512286711-11.4252490661208
Winsorized Mean ( 9 / 24 )-7.6250.667381512286711-11.4252490661208
Winsorized Mean ( 10 / 24 )-7.347222222222220.615450431835296-11.9379593256804
Winsorized Mean ( 11 / 24 )-7.347222222222220.615450431835296-11.9379593256804
Winsorized Mean ( 12 / 24 )-7.513888888888890.592398725705376-12.6838370220024
Winsorized Mean ( 13 / 24 )-7.333333333333330.561199810154154-13.0672412938254
Winsorized Mean ( 14 / 24 )-7.138888888888890.529750862530623-13.4759363199266
Winsorized Mean ( 15 / 24 )-7.138888888888890.529750862530623-13.4759363199266
Winsorized Mean ( 16 / 24 )-7.138888888888890.529750862530623-13.4759363199266
Winsorized Mean ( 17 / 24 )-6.902777777777780.494159837027844-13.9687146962306
Winsorized Mean ( 18 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 19 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 20 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 21 / 24 )-6.652777777777780.459280805672737-14.485207514895
Winsorized Mean ( 22 / 24 )-6.958333333333330.416989311699937-16.6870783928882
Winsorized Mean ( 23 / 24 )-6.958333333333330.416989311699937-16.6870783928882
Winsorized Mean ( 24 / 24 )-6.958333333333330.416989311699937-16.6870783928882
Trimmed Mean ( 1 / 24 )-7.828571428571430.797244589336462-9.81953535123651
Trimmed Mean ( 2 / 24 )-7.735294117647060.771421514627631-10.0273248424772
Trimmed Mean ( 3 / 24 )-7.636363636363640.740325753171868-10.3148696417033
Trimmed Mean ( 4 / 24 )-7.5468750.716490041738693-10.5331191787204
Trimmed Mean ( 5 / 24 )-7.451612903225810.687455558625084-10.8394103585824
Trimmed Mean ( 6 / 24 )-7.383333333333330.663449156625808-11.1287101047558
Trimmed Mean ( 7 / 24 )-7.310344827586210.643364801435695-11.3626745063965
Trimmed Mean ( 8 / 24 )-7.232142857142860.627813703563556-11.5195683306883
Trimmed Mean ( 9 / 24 )-7.166666666666670.614152902428334-11.669189607881
Trimmed Mean ( 10 / 24 )-7.096153846153850.596786022035533-11.8906167104084
Trimmed Mean ( 11 / 24 )-7.060.58721758300984-12.022800754387
Trimmed Mean ( 12 / 24 )-7.020833333333330.574648816078421-12.2176068877086
Trimmed Mean ( 13 / 24 )-6.956521739130430.562908700038354-12.3581705854901
Trimmed Mean ( 14 / 24 )-6.909090909090910.554453602069616-12.4610803921216
Trimmed Mean ( 15 / 24 )-6.880952380952380.549735847191043-12.5168340687835
Trimmed Mean ( 16 / 24 )-6.850.542489513073637-12.6269721993136
Trimmed Mean ( 17 / 24 )-6.815789473684210.531852105077648-12.8151969478228
Trimmed Mean ( 18 / 24 )-6.805555555555560.525265532916968-12.9564099090266
Trimmed Mean ( 19 / 24 )-6.823529411764710.523035477703332-13.0460163844469
Trimmed Mean ( 20 / 24 )-6.843750.518040225661315-13.2108466891031
Trimmed Mean ( 21 / 24 )-6.866666666666670.509074737266156-13.4885237156772
Trimmed Mean ( 22 / 24 )-6.892857142857140.494250771006953-13.9460726157576
Trimmed Mean ( 23 / 24 )-6.884615384615390.484615384615385-14.2063492063492
Trimmed Mean ( 24 / 24 )-6.8750.467465026204782-14.7069825860903
Median-7
Midrange-11.5
Midmean - Weighted Average at Xnp-6.25581395348837
Midmean - Weighted Average at X(n+1)p-6.11904761904762
Midmean - Empirical Distribution Function-6.25581395348837
Midmean - Empirical Distribution Function - Averaging-6.11904761904762
Midmean - Empirical Distribution Function - Interpolation-6.11904761904762
Midmean - Closest Observation-6.25581395348837
Midmean - True Basic - Statistics Graphics Toolkit-6.11904761904762
Midmean - MS Excel (old versions)-6.25581395348837
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')