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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 06:43:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229867062zrv9sl028pc7q8w.htm/, Retrieved Sun, 19 May 2024 09:22:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35580, Retrieved Sun, 19 May 2024 09:22:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Rekenkundig gemid...] [2008-12-21 13:43:28] [00a0a665d7a07edd2e460056b0c0c354] [Current]
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Dataseries X:
2175
2197
2350
2440
2409
2473
2408
2455
2448
2498
2646
2757
2849
2921
2982
3081
3106
3119
3061
3097
3162
3257
3277
3295
3364
3494
3667
3813
3918
3896
3801
3570
3702
3862
3970
4139
4200
4291
4444
4503
4357
4591
4697
4621
4563
4203
4296
4435
4105
4117
3844
3721
3674
3858
3801
3504
3033
3047
2962
2198
2014




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35580&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35580&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3421.9344262295195.647739608780635.7764275478536
Geometric Mean3337.62169110806
Harmonic Mean3250.25578328901
Quadratic Mean3501.22044763691
Winsorized Mean ( 1 / 20 )3423.3278688524694.764429589750436.1246079744538
Winsorized Mean ( 2 / 20 )3423.0655737704994.402170916191736.2604539763118
Winsorized Mean ( 3 / 20 )3421.7377049180394.11038136506136.3587699389386
Winsorized Mean ( 4 / 20 )3427.7704918032891.263865309172837.5589011071478
Winsorized Mean ( 5 / 20 )3427.6885245901689.41096417217938.3363333157827
Winsorized Mean ( 6 / 20 )3426.9016393442689.225062962213438.4073883007014
Winsorized Mean ( 7 / 20 )3421.5081967213186.905823730828239.3702982129102
Winsorized Mean ( 8 / 20 )3414.5573770491885.301229417946940.0294040349526
Winsorized Mean ( 9 / 20 )3414.8524590163984.979588793493540.1843843621641
Winsorized Mean ( 10 / 20 )3403.3770491803382.010065902020741.4995038931735
Winsorized Mean ( 11 / 20 )3407.3442622950881.074434143687242.0273579246485
Winsorized Mean ( 12 / 20 )3424.4590163934473.841891252186446.3755594327637
Winsorized Mean ( 13 / 20 )3443.426229508269.04060917539449.8753743722097
Winsorized Mean ( 14 / 20 )3461.786885245965.183998148469953.1079250057809
Winsorized Mean ( 15 / 20 )3446.2950819672157.162008975268660.2899573291462
Winsorized Mean ( 16 / 20 )3443.4098360655753.480124376309864.3867207906291
Winsorized Mean ( 17 / 20 )3442.8524590163951.747362521240566.5319407844839
Winsorized Mean ( 18 / 20 )3447.8688524590248.094916829267171.688841145077
Winsorized Mean ( 19 / 20 )3450.9836065573847.292257778563972.9714284886943
Winsorized Mean ( 20 / 20 )3450.9836065573845.984913728340175.0459950179392
Trimmed Mean ( 1 / 20 )3424.1864406779793.436099970300636.6473605144732
Trimmed Mean ( 2 / 20 )3425.1052631578991.770092089617737.3226743611973
Trimmed Mean ( 3 / 20 )3426.2363636363689.920656996250238.1028840100584
Trimmed Mean ( 4 / 20 )3427.9622641509487.734028571714839.0722085826583
Trimmed Mean ( 5 / 20 )3428.0196078431486.082356782173439.8225575598209
Trimmed Mean ( 6 / 20 )3428.1020408163384.573968575605640.5337729629153
Trimmed Mean ( 7 / 20 )3428.3617021276682.656145092129341.4773964876583
Trimmed Mean ( 8 / 20 )3429.6888888888980.81516398249442.4386800679118
Trimmed Mean ( 9 / 20 )3432.3720930232678.80981370817643.5525974687994
Trimmed Mean ( 10 / 20 )3435.2682926829376.206555191364245.0783831398301
Trimmed Mean ( 11 / 20 )3440.2564102564173.507908246865446.80117408188
Trimmed Mean ( 12 / 20 )3445.1891891891970.080925313879949.1601555453043
Trimmed Mean ( 13 / 20 )3448.267.497311493299751.0864792050613
Trimmed Mean ( 14 / 20 )3448.8787878787965.253290837363952.853714251358
Trimmed Mean ( 15 / 20 )3447.0645161290363.126327269919454.6058144867175
Trimmed Mean ( 16 / 20 )3447.172413793162.341248017252355.2952102088032
Trimmed Mean ( 17 / 20 )3447.7037037037062.002477085311555.6059026312753
Trimmed Mean ( 18 / 20 )3448.461.655521515378855.9301083705839
Trimmed Mean ( 19 / 20 )3448.4782608695761.874853601143355.7331138607469
Trimmed Mean ( 20 / 20 )3448.0952380952461.881680678760855.7207755231299
Median3494
Midrange3355.5
Midmean - Weighted Average at Xnp3429.63333333333
Midmean - Weighted Average at X(n+1)p3447.06451612903
Midmean - Empirical Distribution Function3447.06451612903
Midmean - Empirical Distribution Function - Averaging3447.06451612903
Midmean - Empirical Distribution Function - Interpolation3447.06451612903
Midmean - Closest Observation3428.375
Midmean - True Basic - Statistics Graphics Toolkit3447.06451612903
Midmean - MS Excel (old versions)3447.06451612903
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3421.93442622951 & 95.6477396087806 & 35.7764275478536 \tabularnewline
Geometric Mean & 3337.62169110806 &  &  \tabularnewline
Harmonic Mean & 3250.25578328901 &  &  \tabularnewline
Quadratic Mean & 3501.22044763691 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3423.32786885246 & 94.7644295897504 & 36.1246079744538 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3423.06557377049 & 94.4021709161917 & 36.2604539763118 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3421.73770491803 & 94.110381365061 & 36.3587699389386 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3427.77049180328 & 91.2638653091728 & 37.5589011071478 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3427.68852459016 & 89.410964172179 & 38.3363333157827 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3426.90163934426 & 89.2250629622134 & 38.4073883007014 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3421.50819672131 & 86.9058237308282 & 39.3702982129102 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3414.55737704918 & 85.3012294179469 & 40.0294040349526 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3414.85245901639 & 84.9795887934935 & 40.1843843621641 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3403.37704918033 & 82.0100659020207 & 41.4995038931735 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3407.34426229508 & 81.0744341436872 & 42.0273579246485 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3424.45901639344 & 73.8418912521864 & 46.3755594327637 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3443.4262295082 & 69.040609175394 & 49.8753743722097 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3461.7868852459 & 65.1839981484699 & 53.1079250057809 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3446.29508196721 & 57.1620089752686 & 60.2899573291462 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3443.40983606557 & 53.4801243763098 & 64.3867207906291 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3442.85245901639 & 51.7473625212405 & 66.5319407844839 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3447.86885245902 & 48.0949168292671 & 71.688841145077 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3450.98360655738 & 47.2922577785639 & 72.9714284886943 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3450.98360655738 & 45.9849137283401 & 75.0459950179392 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3424.18644067797 & 93.4360999703006 & 36.6473605144732 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3425.10526315789 & 91.7700920896177 & 37.3226743611973 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3426.23636363636 & 89.9206569962502 & 38.1028840100584 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3427.96226415094 & 87.7340285717148 & 39.0722085826583 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3428.01960784314 & 86.0823567821734 & 39.8225575598209 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3428.10204081633 & 84.5739685756056 & 40.5337729629153 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3428.36170212766 & 82.6561450921293 & 41.4773964876583 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3429.68888888889 & 80.815163982494 & 42.4386800679118 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3432.37209302326 & 78.809813708176 & 43.5525974687994 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3435.26829268293 & 76.2065551913642 & 45.0783831398301 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3440.25641025641 & 73.5079082468654 & 46.80117408188 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3445.18918918919 & 70.0809253138799 & 49.1601555453043 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3448.2 & 67.4973114932997 & 51.0864792050613 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3448.87878787879 & 65.2532908373639 & 52.853714251358 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3447.06451612903 & 63.1263272699194 & 54.6058144867175 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3447.1724137931 & 62.3412480172523 & 55.2952102088032 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3447.70370370370 & 62.0024770853115 & 55.6059026312753 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3448.4 & 61.6555215153788 & 55.9301083705839 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3448.47826086957 & 61.8748536011433 & 55.7331138607469 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3448.09523809524 & 61.8816806787608 & 55.7207755231299 \tabularnewline
Median & 3494 &  &  \tabularnewline
Midrange & 3355.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3429.63333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3447.06451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3447.06451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3447.06451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3447.06451612903 &  &  \tabularnewline
Midmean - Closest Observation & 3428.375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3447.06451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3447.06451612903 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35580&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]3421.93442622951[/C][C]95.6477396087806[/C][C]35.7764275478536[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3337.62169110806[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3250.25578328901[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3501.22044763691[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3423.32786885246[/C][C]94.7644295897504[/C][C]36.1246079744538[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3423.06557377049[/C][C]94.4021709161917[/C][C]36.2604539763118[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3421.73770491803[/C][C]94.110381365061[/C][C]36.3587699389386[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3427.77049180328[/C][C]91.2638653091728[/C][C]37.5589011071478[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3427.68852459016[/C][C]89.410964172179[/C][C]38.3363333157827[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3426.90163934426[/C][C]89.2250629622134[/C][C]38.4073883007014[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3421.50819672131[/C][C]86.9058237308282[/C][C]39.3702982129102[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3414.55737704918[/C][C]85.3012294179469[/C][C]40.0294040349526[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3414.85245901639[/C][C]84.9795887934935[/C][C]40.1843843621641[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3403.37704918033[/C][C]82.0100659020207[/C][C]41.4995038931735[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3407.34426229508[/C][C]81.0744341436872[/C][C]42.0273579246485[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3424.45901639344[/C][C]73.8418912521864[/C][C]46.3755594327637[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3443.4262295082[/C][C]69.040609175394[/C][C]49.8753743722097[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3461.7868852459[/C][C]65.1839981484699[/C][C]53.1079250057809[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3446.29508196721[/C][C]57.1620089752686[/C][C]60.2899573291462[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3443.40983606557[/C][C]53.4801243763098[/C][C]64.3867207906291[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3442.85245901639[/C][C]51.7473625212405[/C][C]66.5319407844839[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3447.86885245902[/C][C]48.0949168292671[/C][C]71.688841145077[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3450.98360655738[/C][C]47.2922577785639[/C][C]72.9714284886943[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3450.98360655738[/C][C]45.9849137283401[/C][C]75.0459950179392[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3424.18644067797[/C][C]93.4360999703006[/C][C]36.6473605144732[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3425.10526315789[/C][C]91.7700920896177[/C][C]37.3226743611973[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3426.23636363636[/C][C]89.9206569962502[/C][C]38.1028840100584[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3427.96226415094[/C][C]87.7340285717148[/C][C]39.0722085826583[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3428.01960784314[/C][C]86.0823567821734[/C][C]39.8225575598209[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3428.10204081633[/C][C]84.5739685756056[/C][C]40.5337729629153[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3428.36170212766[/C][C]82.6561450921293[/C][C]41.4773964876583[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3429.68888888889[/C][C]80.815163982494[/C][C]42.4386800679118[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3432.37209302326[/C][C]78.809813708176[/C][C]43.5525974687994[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3435.26829268293[/C][C]76.2065551913642[/C][C]45.0783831398301[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3440.25641025641[/C][C]73.5079082468654[/C][C]46.80117408188[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3445.18918918919[/C][C]70.0809253138799[/C][C]49.1601555453043[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3448.2[/C][C]67.4973114932997[/C][C]51.0864792050613[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3448.87878787879[/C][C]65.2532908373639[/C][C]52.853714251358[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3447.06451612903[/C][C]63.1263272699194[/C][C]54.6058144867175[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3447.1724137931[/C][C]62.3412480172523[/C][C]55.2952102088032[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3447.70370370370[/C][C]62.0024770853115[/C][C]55.6059026312753[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3448.4[/C][C]61.6555215153788[/C][C]55.9301083705839[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3448.47826086957[/C][C]61.8748536011433[/C][C]55.7331138607469[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3448.09523809524[/C][C]61.8816806787608[/C][C]55.7207755231299[/C][/ROW]
[ROW][C]Median[/C][C]3494[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3355.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3429.63333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3447.06451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3447.06451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3447.06451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3447.06451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3428.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3447.06451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3447.06451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35580&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 Mean3421.9344262295195.647739608780635.7764275478536
Geometric Mean3337.62169110806
Harmonic Mean3250.25578328901
Quadratic Mean3501.22044763691
Winsorized Mean ( 1 / 20 )3423.3278688524694.764429589750436.1246079744538
Winsorized Mean ( 2 / 20 )3423.0655737704994.402170916191736.2604539763118
Winsorized Mean ( 3 / 20 )3421.7377049180394.11038136506136.3587699389386
Winsorized Mean ( 4 / 20 )3427.7704918032891.263865309172837.5589011071478
Winsorized Mean ( 5 / 20 )3427.6885245901689.41096417217938.3363333157827
Winsorized Mean ( 6 / 20 )3426.9016393442689.225062962213438.4073883007014
Winsorized Mean ( 7 / 20 )3421.5081967213186.905823730828239.3702982129102
Winsorized Mean ( 8 / 20 )3414.5573770491885.301229417946940.0294040349526
Winsorized Mean ( 9 / 20 )3414.8524590163984.979588793493540.1843843621641
Winsorized Mean ( 10 / 20 )3403.3770491803382.010065902020741.4995038931735
Winsorized Mean ( 11 / 20 )3407.3442622950881.074434143687242.0273579246485
Winsorized Mean ( 12 / 20 )3424.4590163934473.841891252186446.3755594327637
Winsorized Mean ( 13 / 20 )3443.426229508269.04060917539449.8753743722097
Winsorized Mean ( 14 / 20 )3461.786885245965.183998148469953.1079250057809
Winsorized Mean ( 15 / 20 )3446.2950819672157.162008975268660.2899573291462
Winsorized Mean ( 16 / 20 )3443.4098360655753.480124376309864.3867207906291
Winsorized Mean ( 17 / 20 )3442.8524590163951.747362521240566.5319407844839
Winsorized Mean ( 18 / 20 )3447.8688524590248.094916829267171.688841145077
Winsorized Mean ( 19 / 20 )3450.9836065573847.292257778563972.9714284886943
Winsorized Mean ( 20 / 20 )3450.9836065573845.984913728340175.0459950179392
Trimmed Mean ( 1 / 20 )3424.1864406779793.436099970300636.6473605144732
Trimmed Mean ( 2 / 20 )3425.1052631578991.770092089617737.3226743611973
Trimmed Mean ( 3 / 20 )3426.2363636363689.920656996250238.1028840100584
Trimmed Mean ( 4 / 20 )3427.9622641509487.734028571714839.0722085826583
Trimmed Mean ( 5 / 20 )3428.0196078431486.082356782173439.8225575598209
Trimmed Mean ( 6 / 20 )3428.1020408163384.573968575605640.5337729629153
Trimmed Mean ( 7 / 20 )3428.3617021276682.656145092129341.4773964876583
Trimmed Mean ( 8 / 20 )3429.6888888888980.81516398249442.4386800679118
Trimmed Mean ( 9 / 20 )3432.3720930232678.80981370817643.5525974687994
Trimmed Mean ( 10 / 20 )3435.2682926829376.206555191364245.0783831398301
Trimmed Mean ( 11 / 20 )3440.2564102564173.507908246865446.80117408188
Trimmed Mean ( 12 / 20 )3445.1891891891970.080925313879949.1601555453043
Trimmed Mean ( 13 / 20 )3448.267.497311493299751.0864792050613
Trimmed Mean ( 14 / 20 )3448.8787878787965.253290837363952.853714251358
Trimmed Mean ( 15 / 20 )3447.0645161290363.126327269919454.6058144867175
Trimmed Mean ( 16 / 20 )3447.172413793162.341248017252355.2952102088032
Trimmed Mean ( 17 / 20 )3447.7037037037062.002477085311555.6059026312753
Trimmed Mean ( 18 / 20 )3448.461.655521515378855.9301083705839
Trimmed Mean ( 19 / 20 )3448.4782608695761.874853601143355.7331138607469
Trimmed Mean ( 20 / 20 )3448.0952380952461.881680678760855.7207755231299
Median3494
Midrange3355.5
Midmean - Weighted Average at Xnp3429.63333333333
Midmean - Weighted Average at X(n+1)p3447.06451612903
Midmean - Empirical Distribution Function3447.06451612903
Midmean - Empirical Distribution Function - Averaging3447.06451612903
Midmean - Empirical Distribution Function - Interpolation3447.06451612903
Midmean - Closest Observation3428.375
Midmean - True Basic - Statistics Graphics Toolkit3447.06451612903
Midmean - MS Excel (old versions)3447.06451612903
Number of observations61



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')