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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 15 Oct 2009 15:56:32 -0600
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/Oct/15/t1255643853ut89i71m4sgu7fm.htm/, Retrieved Sat, 04 May 2024 12:59:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46895, Retrieved Sat, 04 May 2024 12:59:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendensy] [2009-10-15 21:56:32] [ea241b681aafed79da4b5b99fad98471] [Current]
- RMP     [Kernel Density Estimation] [kernel-density] [2009-10-15 22:50:04] [cd6314e7e707a6546bd4604c9d1f2b69]
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Dataseries X:
216234
213587
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
208795
197922
194596
194581
185686
178106
172608
167302
168053
202300
202388
182516
173476
166444
171297
169701
164182
161914
159612
151001
158114
186530
187069
174330
169362
166827
178037
186412
189226
191563
188906
186005
195309
223532
226899
214126




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46895&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46895&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean204728.7826086963442.2094339598159.4759809176346
Geometric Mean202745.982133958
Harmonic Mean200757.671262276
Quadratic Mean206687.186883878
Winsorized Mean ( 1 / 23 )204751.6086956523399.8448624539160.2238093146017
Winsorized Mean ( 2 / 23 )204683.1159420293365.0800440891660.8256306715673
Winsorized Mean ( 3 / 23 )204443.1159420293273.3753651441062.4563617478771
Winsorized Mean ( 4 / 23 )204333.2028985513202.4743684194463.8047894820148
Winsorized Mean ( 5 / 23 )204414.7971014493157.823838359164.7328057437394
Winsorized Mean ( 6 / 23 )204287.4057971013123.3115971742265.4073086982189
Winsorized Mean ( 7 / 23 )204298.8695652173108.4310996178165.7241106583756
Winsorized Mean ( 8 / 23 )204330.5217391303083.6543403283866.2624597922254
Winsorized Mean ( 9 / 23 )204424.5652173913041.1628456466867.219210411576
Winsorized Mean ( 10 / 23 )204063.4057971012963.7026290380368.8542108772016
Winsorized Mean ( 11 / 23 )204003.1449275362869.5955647350771.0912532185943
Winsorized Mean ( 12 / 23 )203941.0579710142785.7085885875273.2097602766202
Winsorized Mean ( 13 / 23 )203771.1159420292707.2406004269975.2689346893993
Winsorized Mean ( 14 / 23 )203695.840579712641.2859504666777.1199500545256
Winsorized Mean ( 15 / 23 )204452.5797101452505.4314314029881.6037418336596
Winsorized Mean ( 16 / 23 )204211.4202898552464.1844541436882.8718077278918
Winsorized Mean ( 17 / 23 )204790.159420292223.7410759381792.0926278855964
Winsorized Mean ( 18 / 23 )205542.7681159422093.9987403767698.158018986659
Winsorized Mean ( 19 / 23 )204703.4637681161946.05434691165105.188975884963
Winsorized Mean ( 20 / 23 )204284.0434782611854.02883634978110.183854464991
Winsorized Mean ( 21 / 23 )203642.4782608701757.31129692262115.882984771956
Winsorized Mean ( 22 / 23 )203770.0144927541726.92005926393117.996205672431
Winsorized Mean ( 23 / 23 )204370.3478260871639.27834469950124.670925158565
Trimmed Mean ( 1 / 23 )204618.5074626873327.8533201836361.4866365117906
Trimmed Mean ( 2 / 23 )204477.2153846153241.3620527437963.083732103153
Trimmed Mean ( 3 / 23 )204364.4603174603159.5358799781264.6817976059431
Trimmed Mean ( 4 / 23 )204334.8032786893102.5855217179165.8595232422627
Trimmed Mean ( 5 / 23 )204335.2711864413058.4132026009366.8108779456845
Trimmed Mean ( 6 / 23 )204316.0175438603016.9283014761367.7231929721006
Trimmed Mean ( 7 / 23 )2043222973.894999040868.7051829556532
Trimmed Mean ( 8 / 23 )204326.3018867922922.7288707556269.9094274297046
Trimmed Mean ( 9 / 23 )204325.5882352942863.4651690314171.3560585423182
Trimmed Mean ( 10 / 23 )204310.1020408162797.7455861825973.0266908649078
Trimmed Mean ( 11 / 23 )204310.1020408162731.3646692853374.8014735411639
Trimmed Mean ( 12 / 23 )204394.1555555562666.8861400130176.6415005458608
Trimmed Mean ( 13 / 23 )204454.7441860472601.2475193266278.5987272133846
Trimmed Mean ( 14 / 23 )204543.2439024392531.7783094633180.7903453228488
Trimmed Mean ( 15 / 23 )204650.3333333332453.4860869500483.4120618909794
Trimmed Mean ( 16 / 23 )204674.9189189192381.117523607185.9575039407806
Trimmed Mean ( 17 / 23 )204732.0285714292290.3446276535389.3891801694394
Trimmed Mean ( 18 / 23 )204724.8787878792228.5834264294591.8632331013434
Trimmed Mean ( 19 / 23 )204623.7419354842172.710796765794.1790054341733
Trimmed Mean ( 20 / 23 )204613.7586206902130.6011337810096.0356940473313
Trimmed Mean ( 21 / 23 )204655.8888888892089.0101162768397.9678783239403
Trimmed Mean ( 22 / 23 )204655.8888888892047.5945089462199.9494226003833
Trimmed Mean ( 23 / 23 )204928.0434782611983.22825767698103.330538320536
Median204045
Midrange208423
Midmean - Weighted Average at Xnp204071.676470588
Midmean - Weighted Average at X(n+1)p204732.028571429
Midmean - Empirical Distribution Function204732.028571429
Midmean - Empirical Distribution Function - Averaging204732.028571429
Midmean - Empirical Distribution Function - Interpolation204732.028571429
Midmean - Closest Observation203992.416666667
Midmean - True Basic - Statistics Graphics Toolkit204732.028571429
Midmean - MS Excel (old versions)204732.028571429
Number of observations69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 204728.782608696 & 3442.20943395981 & 59.4759809176346 \tabularnewline
Geometric Mean & 202745.982133958 &  &  \tabularnewline
Harmonic Mean & 200757.671262276 &  &  \tabularnewline
Quadratic Mean & 206687.186883878 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 204751.608695652 & 3399.84486245391 & 60.2238093146017 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 204683.115942029 & 3365.08004408916 & 60.8256306715673 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 204443.115942029 & 3273.37536514410 & 62.4563617478771 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 204333.202898551 & 3202.47436841944 & 63.8047894820148 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 204414.797101449 & 3157.8238383591 & 64.7328057437394 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 204287.405797101 & 3123.31159717422 & 65.4073086982189 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 204298.869565217 & 3108.43109961781 & 65.7241106583756 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 204330.521739130 & 3083.65434032838 & 66.2624597922254 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 204424.565217391 & 3041.16284564668 & 67.219210411576 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 204063.405797101 & 2963.70262903803 & 68.8542108772016 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 204003.144927536 & 2869.59556473507 & 71.0912532185943 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 203941.057971014 & 2785.70858858752 & 73.2097602766202 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 203771.115942029 & 2707.24060042699 & 75.2689346893993 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 203695.84057971 & 2641.28595046667 & 77.1199500545256 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 204452.579710145 & 2505.43143140298 & 81.6037418336596 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 204211.420289855 & 2464.18445414368 & 82.8718077278918 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 204790.15942029 & 2223.74107593817 & 92.0926278855964 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 205542.768115942 & 2093.99874037676 & 98.158018986659 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 204703.463768116 & 1946.05434691165 & 105.188975884963 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 204284.043478261 & 1854.02883634978 & 110.183854464991 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 203642.478260870 & 1757.31129692262 & 115.882984771956 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 203770.014492754 & 1726.92005926393 & 117.996205672431 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 204370.347826087 & 1639.27834469950 & 124.670925158565 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 204618.507462687 & 3327.85332018363 & 61.4866365117906 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 204477.215384615 & 3241.36205274379 & 63.083732103153 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 204364.460317460 & 3159.53587997812 & 64.6817976059431 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 204334.803278689 & 3102.58552171791 & 65.8595232422627 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 204335.271186441 & 3058.41320260093 & 66.8108779456845 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 204316.017543860 & 3016.92830147613 & 67.7231929721006 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 204322 & 2973.8949990408 & 68.7051829556532 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 204326.301886792 & 2922.72887075562 & 69.9094274297046 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 204325.588235294 & 2863.46516903141 & 71.3560585423182 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 204310.102040816 & 2797.74558618259 & 73.0266908649078 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 204310.102040816 & 2731.36466928533 & 74.8014735411639 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 204394.155555556 & 2666.88614001301 & 76.6415005458608 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 204454.744186047 & 2601.24751932662 & 78.5987272133846 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 204543.243902439 & 2531.77830946331 & 80.7903453228488 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 204650.333333333 & 2453.48608695004 & 83.4120618909794 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 204674.918918919 & 2381.1175236071 & 85.9575039407806 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 204732.028571429 & 2290.34462765353 & 89.3891801694394 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 204724.878787879 & 2228.58342642945 & 91.8632331013434 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 204623.741935484 & 2172.7107967657 & 94.1790054341733 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 204613.758620690 & 2130.60113378100 & 96.0356940473313 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 204655.888888889 & 2089.01011627683 & 97.9678783239403 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 204655.888888889 & 2047.59450894621 & 99.9494226003833 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 204928.043478261 & 1983.22825767698 & 103.330538320536 \tabularnewline
Median & 204045 &  &  \tabularnewline
Midrange & 208423 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 204071.676470588 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 204732.028571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 204732.028571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 204732.028571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 204732.028571429 &  &  \tabularnewline
Midmean - Closest Observation & 203992.416666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 204732.028571429 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 204732.028571429 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46895&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]204728.782608696[/C][C]3442.20943395981[/C][C]59.4759809176346[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]202745.982133958[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]200757.671262276[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]206687.186883878[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]204751.608695652[/C][C]3399.84486245391[/C][C]60.2238093146017[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]204683.115942029[/C][C]3365.08004408916[/C][C]60.8256306715673[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]204443.115942029[/C][C]3273.37536514410[/C][C]62.4563617478771[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]204333.202898551[/C][C]3202.47436841944[/C][C]63.8047894820148[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]204414.797101449[/C][C]3157.8238383591[/C][C]64.7328057437394[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]204287.405797101[/C][C]3123.31159717422[/C][C]65.4073086982189[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]204298.869565217[/C][C]3108.43109961781[/C][C]65.7241106583756[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]204330.521739130[/C][C]3083.65434032838[/C][C]66.2624597922254[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]204424.565217391[/C][C]3041.16284564668[/C][C]67.219210411576[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]204063.405797101[/C][C]2963.70262903803[/C][C]68.8542108772016[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]204003.144927536[/C][C]2869.59556473507[/C][C]71.0912532185943[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]203941.057971014[/C][C]2785.70858858752[/C][C]73.2097602766202[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]203771.115942029[/C][C]2707.24060042699[/C][C]75.2689346893993[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]203695.84057971[/C][C]2641.28595046667[/C][C]77.1199500545256[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]204452.579710145[/C][C]2505.43143140298[/C][C]81.6037418336596[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]204211.420289855[/C][C]2464.18445414368[/C][C]82.8718077278918[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]204790.15942029[/C][C]2223.74107593817[/C][C]92.0926278855964[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]205542.768115942[/C][C]2093.99874037676[/C][C]98.158018986659[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]204703.463768116[/C][C]1946.05434691165[/C][C]105.188975884963[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]204284.043478261[/C][C]1854.02883634978[/C][C]110.183854464991[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]203642.478260870[/C][C]1757.31129692262[/C][C]115.882984771956[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]203770.014492754[/C][C]1726.92005926393[/C][C]117.996205672431[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]204370.347826087[/C][C]1639.27834469950[/C][C]124.670925158565[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]204618.507462687[/C][C]3327.85332018363[/C][C]61.4866365117906[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]204477.215384615[/C][C]3241.36205274379[/C][C]63.083732103153[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]204364.460317460[/C][C]3159.53587997812[/C][C]64.6817976059431[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]204334.803278689[/C][C]3102.58552171791[/C][C]65.8595232422627[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]204335.271186441[/C][C]3058.41320260093[/C][C]66.8108779456845[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]204316.017543860[/C][C]3016.92830147613[/C][C]67.7231929721006[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]204322[/C][C]2973.8949990408[/C][C]68.7051829556532[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]204326.301886792[/C][C]2922.72887075562[/C][C]69.9094274297046[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]204325.588235294[/C][C]2863.46516903141[/C][C]71.3560585423182[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]204310.102040816[/C][C]2797.74558618259[/C][C]73.0266908649078[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]204310.102040816[/C][C]2731.36466928533[/C][C]74.8014735411639[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]204394.155555556[/C][C]2666.88614001301[/C][C]76.6415005458608[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]204454.744186047[/C][C]2601.24751932662[/C][C]78.5987272133846[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]204543.243902439[/C][C]2531.77830946331[/C][C]80.7903453228488[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]204650.333333333[/C][C]2453.48608695004[/C][C]83.4120618909794[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]204674.918918919[/C][C]2381.1175236071[/C][C]85.9575039407806[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]204732.028571429[/C][C]2290.34462765353[/C][C]89.3891801694394[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]204724.878787879[/C][C]2228.58342642945[/C][C]91.8632331013434[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]204623.741935484[/C][C]2172.7107967657[/C][C]94.1790054341733[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]204613.758620690[/C][C]2130.60113378100[/C][C]96.0356940473313[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]204655.888888889[/C][C]2089.01011627683[/C][C]97.9678783239403[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]204655.888888889[/C][C]2047.59450894621[/C][C]99.9494226003833[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]204928.043478261[/C][C]1983.22825767698[/C][C]103.330538320536[/C][/ROW]
[ROW][C]Median[/C][C]204045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]208423[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]204071.676470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]204732.028571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]204732.028571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]204732.028571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]204732.028571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]203992.416666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]204732.028571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]204732.028571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46895&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 Mean204728.7826086963442.2094339598159.4759809176346
Geometric Mean202745.982133958
Harmonic Mean200757.671262276
Quadratic Mean206687.186883878
Winsorized Mean ( 1 / 23 )204751.6086956523399.8448624539160.2238093146017
Winsorized Mean ( 2 / 23 )204683.1159420293365.0800440891660.8256306715673
Winsorized Mean ( 3 / 23 )204443.1159420293273.3753651441062.4563617478771
Winsorized Mean ( 4 / 23 )204333.2028985513202.4743684194463.8047894820148
Winsorized Mean ( 5 / 23 )204414.7971014493157.823838359164.7328057437394
Winsorized Mean ( 6 / 23 )204287.4057971013123.3115971742265.4073086982189
Winsorized Mean ( 7 / 23 )204298.8695652173108.4310996178165.7241106583756
Winsorized Mean ( 8 / 23 )204330.5217391303083.6543403283866.2624597922254
Winsorized Mean ( 9 / 23 )204424.5652173913041.1628456466867.219210411576
Winsorized Mean ( 10 / 23 )204063.4057971012963.7026290380368.8542108772016
Winsorized Mean ( 11 / 23 )204003.1449275362869.5955647350771.0912532185943
Winsorized Mean ( 12 / 23 )203941.0579710142785.7085885875273.2097602766202
Winsorized Mean ( 13 / 23 )203771.1159420292707.2406004269975.2689346893993
Winsorized Mean ( 14 / 23 )203695.840579712641.2859504666777.1199500545256
Winsorized Mean ( 15 / 23 )204452.5797101452505.4314314029881.6037418336596
Winsorized Mean ( 16 / 23 )204211.4202898552464.1844541436882.8718077278918
Winsorized Mean ( 17 / 23 )204790.159420292223.7410759381792.0926278855964
Winsorized Mean ( 18 / 23 )205542.7681159422093.9987403767698.158018986659
Winsorized Mean ( 19 / 23 )204703.4637681161946.05434691165105.188975884963
Winsorized Mean ( 20 / 23 )204284.0434782611854.02883634978110.183854464991
Winsorized Mean ( 21 / 23 )203642.4782608701757.31129692262115.882984771956
Winsorized Mean ( 22 / 23 )203770.0144927541726.92005926393117.996205672431
Winsorized Mean ( 23 / 23 )204370.3478260871639.27834469950124.670925158565
Trimmed Mean ( 1 / 23 )204618.5074626873327.8533201836361.4866365117906
Trimmed Mean ( 2 / 23 )204477.2153846153241.3620527437963.083732103153
Trimmed Mean ( 3 / 23 )204364.4603174603159.5358799781264.6817976059431
Trimmed Mean ( 4 / 23 )204334.8032786893102.5855217179165.8595232422627
Trimmed Mean ( 5 / 23 )204335.2711864413058.4132026009366.8108779456845
Trimmed Mean ( 6 / 23 )204316.0175438603016.9283014761367.7231929721006
Trimmed Mean ( 7 / 23 )2043222973.894999040868.7051829556532
Trimmed Mean ( 8 / 23 )204326.3018867922922.7288707556269.9094274297046
Trimmed Mean ( 9 / 23 )204325.5882352942863.4651690314171.3560585423182
Trimmed Mean ( 10 / 23 )204310.1020408162797.7455861825973.0266908649078
Trimmed Mean ( 11 / 23 )204310.1020408162731.3646692853374.8014735411639
Trimmed Mean ( 12 / 23 )204394.1555555562666.8861400130176.6415005458608
Trimmed Mean ( 13 / 23 )204454.7441860472601.2475193266278.5987272133846
Trimmed Mean ( 14 / 23 )204543.2439024392531.7783094633180.7903453228488
Trimmed Mean ( 15 / 23 )204650.3333333332453.4860869500483.4120618909794
Trimmed Mean ( 16 / 23 )204674.9189189192381.117523607185.9575039407806
Trimmed Mean ( 17 / 23 )204732.0285714292290.3446276535389.3891801694394
Trimmed Mean ( 18 / 23 )204724.8787878792228.5834264294591.8632331013434
Trimmed Mean ( 19 / 23 )204623.7419354842172.710796765794.1790054341733
Trimmed Mean ( 20 / 23 )204613.7586206902130.6011337810096.0356940473313
Trimmed Mean ( 21 / 23 )204655.8888888892089.0101162768397.9678783239403
Trimmed Mean ( 22 / 23 )204655.8888888892047.5945089462199.9494226003833
Trimmed Mean ( 23 / 23 )204928.0434782611983.22825767698103.330538320536
Median204045
Midrange208423
Midmean - Weighted Average at Xnp204071.676470588
Midmean - Weighted Average at X(n+1)p204732.028571429
Midmean - Empirical Distribution Function204732.028571429
Midmean - Empirical Distribution Function - Averaging204732.028571429
Midmean - Empirical Distribution Function - Interpolation204732.028571429
Midmean - Closest Observation203992.416666667
Midmean - True Basic - Statistics Graphics Toolkit204732.028571429
Midmean - MS Excel (old versions)204732.028571429
Number of observations69



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')