STUDIES
ON
THE
HISTORY
ANALYSIS IN ANCIENT CHINA
OF
STATISTIGAL
Peng Daobin
The statistical anal) sk enjoys a long bistory in China, and it was in tbc Western /hou 1)J,nast! ,
about 3.000 years ago in C’hina, the averages got an application and the gtwtping conc~pt tlxtt
connotes the statistical grouping metbod had been put fwwtrd. In the period ol‘ the Sprmg and
Autumn and Warring States (770 to __
‘3 1 B .C . ) , Mr. Guan Zhotw bad proposcd to set up tbc fout
groups of’ ‘*soldiers, farmers, b orket-s and businessmen” according to their dif’l’ercnt occupatiow.,
and the present classitkation of- population based on tbc sections ot‘ national econotn> migralcs
do-n from such a basic line. With refk-ence to tbc data from investigation. Mr. Surt 14 u txid
completed the high1) cffectke statistical analysis wer the riw and decline of sis sfate:, in .fin
Dylast). Moreover. tbc fortxasting conccpt of economic circular flow proposed bb Mr. I~II Lin in
ancient C’hina to havre a business forecasting according to fhe relationship lxtuwn
tht 4 itnat ic
carlkr 1Itan Il-tc
change and agricultural bumper hanest or trop failure is just 2,300 or morc yrs
Europe and America.
In the Qin Dyas@ ( 22 1 to 206 B.C’.), the metbod ot‘ c)l erall balancc ~itnesscd a t’airll high
lewl of application. The accounting of tinancial incomc and cspenses at that time ws: the amottnt
in treasury at the beginning of current year plus the income rlf-current year minus the esptwes of
currcnt year quals to the amount in treasury at the end of currcnt year.
And it was in the I Ian I$tasty (306 EK. to 220 A.D. ) that the currenq started to be taken as
the measuring-unit. and tbc different physical tneasuring-units nere uni tied for comprehenst i c
calculation. Besides. tbc absolute number and relatke number also prevailed in application at tllat
time. for example, Emperor Liu Bang ot‘ the Han Di nastb special 11,ccorkcd oul tbc tas policies o 1‘
+‘one-fifteenth over the farm rent-‘. Meanwhile, the mathematits showed a prominent dwelopmcnt
and achievement in the ancient China ot‘ that tinne, and Iaid a solid mathematital foundation tiltstatistical analysis. For instance. the “Zhoubi ArithmeGc Classics”, know to the publit in ihe tirst
centur) H.C., is the earliest mathematital uorks in China up till now. In the “Jiuzhang Aritt-inieK’,
there is an account of the uorld adwnced mcthods at that titnc for tbc ti)ur fundatncntal c~pxttiws
of fractional arithmetic, proportioning, squaring, cubage. estraction o 1‘syuare twt and r:ut-ic rwt.
and sur\ ey b> the PI thngorcan theorem. etc..
Si Maqian bad niade out the statistkal charts consisting of tarious fàctors. tkr vhicf-t tbc m:tin
title and items present in line and cohttun, target names, urlit and sequencial order art‘ al 1 e~.~~t-es_;I~~
stipulated for a simple and concise anal>sis to the tfssmce
in things. instead of’ the ~upt~~~flu~~it~
verbal dcscription.
Mr. Fu Xuan( 2 17 to 278 A.D.) had c\er launched a statistical analysis inta tbc tnalprxtice in
the preliminary stage of’ Western .lin D>~nast>to have garrixon troops or fartners opcn up ~x+teland
and grou food grain. [le pointcd out that tbc emphasis should not be Raid onl‘ on the crtlarging of
farmland. bu{ on the itlletlsi\re and mcticulous farming ler an increasc of‘grain ) ield h-cjm a ciefitiilc
unil area of farmland.
In 439 A.D. \+hen the Northern Wci had unitied tbc Huanghc Valle>!, tbc househ&~, in tbc
Central F’lains werc classified into nine gradcs, and the g0\ crnmel;t ~ould tax 0n tbc fat-ni rt:ntcrs
bascd on the proportional difkrence of awrage amount to be paid respecti~~eI> bl rhese renters of’
ninc gradcs. Le. the metbod of wightcd arithmetic mean just in the formula of x = X xfi 1 1%.
In the period of South<rn c)i (479 to 50 2 A.D. 1. TUr. Niao %hiCang bad rcwai~d. G~CI ‘1
comparative anal)sis, the sewre t‘xploitation then bl, miscclIancous Ie\ries. And in tbc pct*ioJd th
Northern Qi (5.50 to 557 Al).), tbc classification of*population OII ages ah shcwed its pri,pcrties oi’
creatkeness and scientiticalness to a ccrtain degree. In tbc Sui l>>nastl (58 1 to 61 8 Al>.). ;i IIW
metbod of the household taues and cor& was formulatcd in the light of’ the statistid
gr~iupiug
metbod, and as for the statistic loork in gc~vcrnmental barns. a ba1ance analysis \cas adoptcd Iiw tix
“deliccr~, storage and surplus”.
In tk Tang Dynasti (618 to 917 Al).), the mcthod of‘ statistical analbsis sa\+’ CI\ igorom
dewiopment, and according to the metbod ot‘comparatiw anal>rsis, Mr. Lu Zhi had dcepl? rc\ealt:d
that the main cause ot‘too much differente between the poor and the rich itas just a rc’suII d sa crc
exploitation by landlord elass, and he reminded the societjr ot‘tcrrible harmfulness from the \:\treme
disparit) between the rich and the poor. F’irstly in addition to the calculation ot‘ comparatij c‘
relatives, had had calculated the ratio of governmcntal tax and landlord3 high or medium land rent,
and as a res&, revealed the outstanding differente 04‘the two: sccondly, the comparatiw rc’lati\ cs
are representcd hy multiple unit for the reason of toa much di tterence of numerawr and
denominator in value.
Also in tbc Tung Dlnasty, the methed oi‘intensit~ analqsis had got an application in 1he process
of calculating intcnsitj relatives. As show n in “NU+ Ewnomic Ilistor! of tbc ‘Tang Dyna@‘, it hiid
been known in calculation that OIICsoldicr ws supported generally b> two houscholds in tht: pt‘riod
of 806 to 830 A.D.. but bj threc households in the period ot‘ 821 to 824 AJ>.. t‘t’om(hat. tbc mayjr
cause of’ hear j burden on peoplt: and national financiatl uorsc-oi’f has just the incrcase ()f iniL+)
expenditures.
From the mid-term of the Tang Dynast>. the “Wi~ctor settlement of accounts” as dcwrihed in
the balante analysis started to transit to tbc “4-factor settlement of‘ accountsY i.c. to di\ ide fhe
“income” into the old haiance and current income, and togcther Gth the “expenditurc-’ arid -‘closing
balance”. the four fastors thus t’ornwd. Mr. Liu Yan is the first person in tbc (‘hinesc st,itistic,ii
wtwrk
bistory to engage in business investigation. He bad set up the business inf&matiw
nation&ide for a prompt master of business trends, and sub_ject to a statistical anal>% tht- wleva~~t
mt’asurt’s uould be \\orked out to stabilizc tbc price.
Rut in the period ofthc Fi\rtz Dyasties (907 to 960 A.D.), the metbod of grouping acwrding to
the different areas pre\ ailed extensi\ el). and the “lo\wr limit or belou to upper limit” disa~ycan:d
in the dcscription, but the “upper limit or bclow to lowr linlit” appcarcd in the statisticC.il lmaly~is
inta the quantity of‘salt o\vned bb, pri\rate dealcrs in tbc period of the Later %hou.
The statistical analisis shoited an outstanding dclelopment in the Sang Dylast!, mainI> in the
following three aspects:
1, Inno\rations
ndt:
in the statisticai grouping. sueh as the originalit! in classiC_atwn and
originality in frequenc‘ distribution chart.
a. Originality in classi tication
The classified catalogue of tases was initiated in the Sang D>nast]r . .4ccording tr) that, tbc taws
included the four nia.jor categorics like thti grains. silks. metals and produw and cach major
catcgor1 \vas re-diFrided inta a ccrtain numbers of‘typw then cach typ< \+as rc-di1 ided a~:ain
intij a
.I
certain nurnbcr of‘ speci fic items:
b. Originality in frequenc~ distribution chart
In the Sang Dlnast‘, a wnlplete freqwnc> distribution chart nas created @st on the bask ofIk
grouping on quantitati\ t: im&. IIIthis chart. the business tahes wrt’ grouped in such ii nwner c)f
referring to the amount of leby. and listad in an appropriatt’ order, then the quantit> ofo~er;~Il units
from each group l+as listed to c]arif> the distrihutic,n status and characteristics ot‘ each bwklcss
7
taxation ilnit.
2. Extensive application ofcomparatice analysis
The comparatiw analyis ws quitc cstcnsive in application in the Sang Dynast!~. m;iinl> in tbc
fields of struttural analysis. intensit) analq5is and djqamic
anal>yis.
3. Application
and dwelopnient ot‘cquilihrium analyis
With reterence to the statistical data concerning the graitl price and purch:tsity qu~mtit! , h81r.
Shen Kuo had ewr adopted the median to decide tbc wa~ of‘ purchasing grains at an appr~~pri;ltt’
pricr so as to prsk ent tbc ncptiw
c‘f‘fi‘cts on the quantitv
of‘grains purchascd h! the statt dw to IIN~
fluctuation of-grain pricc.
Whilc in tbc Yuan Dyasty ( 12Uh tu 1368 A.D.). tbc statistical grouping U~‘Squitc cw~plicatcd.
For example, the owouping on hr~schold rrrades ws adoptcd in considcration of‘ thc,ir ci tal 11~.
Another grouping metbod was to rckr tv ti~e occupations. f’or example, the comnwn I~~uwh~&.t,
soldier. crafisman. salt dealw. medkal workcr and intttllcctwl. etc..
The statistical analysis in the Ming Dbnasty ( 1368 to 1644 A.D.) registered ;t \ igorws
dewlopment.
In 1573, Mr, Zhang Jwheng conductcd a statistical analysis info thi- lhnci,d
conditions then. and as a result of‘ tomparison of finantial income and expenditurcs he f’otlnd tk
problems existed. Also. Mr. Xu Guangqi carried out a statistkal analqsis inta tbc monthl! d;lta
regarding the plagw o1‘locusts, and he hund
the lau that tbc cxtensiL+ harmfiol plnguc ot ICKULS
occurred mast f?equentl>r in the period of‘ late summer and carl> autumn uhen the trops we~c in tbc
maturation stage.
In the Qing dylast> ( 1616 to 191 1 A.D.). the statisticnl aggrcgatc indcxes graduall) dewlolwi
towards a unif‘orm measuring urlit in the form ofcurrcncy. and the figurcs 01’ \ ariow nncas~~~*etnt’~-~fs
were expressly stipulated thcn, uhich Ikilitated the comprehcnsi\ e report of- statistkal :wounting
and the de\~elopment 01’statistical anal- sis as well. In the carl- period of tbc Qing Dyasrq. Mr. t 111
Yanwu got the maximum limit 01‘private land rent per mu from the statistkal anal> sk. Vr. 1,in
Zesu had evor started the statistical anal+
into tbc hakards of opium. and he had succr~sti~lly
ofa people
per yr. It w~s just such a kind ot‘statistical anal\& inta tbc in\cestigation dara {hat h;id
playd an important role in ha\ ing tbc Empcror Diro (iuang dccidc to launch tbc canlpaigi-V ot‘ lwn
on opium-smoking and opium trade. Mortwwr, with ref’ercncc to tbc statistical data. Mr. Rw Shliu
had analyzed in a particular caw tbc caust’ of people’s pol erty and he fkmd that tbc pcopll:‘s
povert>’ was just tbc result of‘tobacco. C+ine and opium.
Af-ter the Opium War. Mr. Wei k’uan carried out the statistkal anal) sis \+ith the wst~~t*n
economic theory as his guidante. Ile bad wer madc a statistical analysis into tbc spclsif‘ic traclc
balante betu-sen import and export commodities bj rekrring to the trade halancc conccpt. Lind iw
had verified and prov4 the existcncc ot‘outflow of sil\ er ingot due to the opium trade. Eksiks, hlr.
Wang Shiduo had madc an anal> sis into the data of population dorn the ages so as to lind the 1,~
of population gro\+th. through that hc had niade a correct judgmcnt that tbc population gro\i th r,ite
would be doubled everj thirtj yars.