Formule Statistica

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<p>ntrebri recapitulative</p> <p>RELAII DE CALCUL</p> <p> ;</p> <p>; ; ; </p> <p>;</p> <p> ; .</p> <p>sau</p> <p>.</p> <p>;</p> <p> .</p> <p>; ;</p> <p>; ; de dinamic:</p> <p>;</p> <p>;</p> <p>; </p> <p>.</p> <p>;</p> <p>. .</p> <p>; </p> <p>.</p> <p>;</p> <p>.</p> <p>;</p> <p>.</p> <p>;</p> <p>;</p> <p>;</p> <p>;</p> <p> mediala:</p> <p>;</p> <p> (1. INDICATORII VARIAIEI I AI VARIABILITII: indicatorii sintetici ai variaiei:Pentru serii simplePentru serii de frecven</p> <p>-abaterea medie liniar:</p> <p>-abaterea medie liniar:</p> <p>-dispersia:</p> <p>-dispersia:</p> <p>-dispersia caracteristicii alternative:</p> <p>-abaterea medie ptratic:</p> <p>; </p> <p>-abaterea medie ptratic:</p> <p>; </p> <p>-coeficientul de variaie: </p> <p>( [0; 100]</p> <p>-coeficientul de variaie:</p> <p>( [0; 100]</p> <p> indicatorii simpli ai variaiei: amplitudinea absolut a variaiei:</p> <p>; amplitudinea relativ a variaiei:</p> <p>; abaterile individuale absolute:</p> <p>; abaterile individuale relative:</p> <p>; abaterea interquartilic:</p> <p>A = Q3 Q1; abaterea interquantilic:</p> <p>. dispersiile n cazul seriilor bidimensionale:</p> <p> dispersiile de grup:</p> <p>; media dispersiilor de grup:</p> <p>; dispersia dintre grupe:</p> <p>; dispersia total:</p> <p>. regula de adunare a dispersiilor:</p> <p>. gradul de determinaie :</p> <p>. gradul de nedeterminaie:</p> <p>;R2 + N2 = 100.2. INDICATORII ASIMETRIEI: asimetrie absolut:</p> <p>. coeficientul de asimetrie propus de Pearson:</p> <p>;</p> <p>. coeficientul de asimetrie propus de Fisher:</p> <p>(3 = moment centrat de ordin 3 = </p> <p>= </p> <p>(2 = moment centrat de ordin 2 = </p> <p>= </p> <p>3. SONDAJUL STATISTIC:Denumirea indicatoruluiCaracteristic nealternativCaracteristic alternativ</p> <p>Colectivitatea generalEantionColectivitatea generalEantion</p> <p>Medie</p> <p>Dispersie</p> <p>Abaterea medie ptratic</p> <p> eroarea medie de reprezentativitate:Pentru sondaj simpluPentru sondaj stratificat</p> <p>-repetat</p> <p>-repetat</p> <p>-nerepetat</p> <p>-nerepetat</p> <p> eroarea limit maxim admis:</p> <p> pentru sondaj simplu:</p> <p> pentru sondaj stratificat:</p> <p> intervalul de ncredere al mediei colectivitii generale: pentru selecia simpl:</p> <p> pentru selecia stratificat:</p> <p> pentru caracteristica alternativ:</p> <p> intervalul de ncredere al nivelului totalizat al caracteristicii la nivelul colectivitii generale: pentru selecia simpl:</p> <p> pentru selecia stratificat:</p> <p> pentru caracteristica alternativ:</p> <p>. redimensionarea eantionului cnd se modific eroarea:</p> <p>Pentru sondajul simpluPentru sondajul stratificat</p> <p>-pentru selecia repetat</p> <p>-pentru selecia repetat</p> <p>-pentru selecia nerepetat</p> <p>-pentru selecia nerepetat</p> <p> redimensionarea eantionului cnd se modific probabilitatea cu care se garanteaz rezultatele i implicit z:</p> <p>Pentru sondajul simpluPentru sondajul stratificat</p> <p>-pentru selecia repetat</p> <p>-pentru selecia repetat</p> <p>-pentru selecia nerepetat</p> <p>-pentru selecia nerepetat</p> <p>4. ANALIZA LEGTURILOR DINTRE FENOMENE: coeficientul de corelaie al rangurilor Spearman:</p> <p>; . coeficientul de corelaie al rangurilor Kendall:</p> <p>; ; Si = Pi Qi i . coeficientul de asociere propus de Yule:</p> <p>;</p> <p>. coeficientul de corelaie propus de Pearson:</p> <p>; </p> <p>sau: .</p> <p>- covariana dintre x i y;</p> <p>- variana lui x;</p> <p>- variana lui y. estimarea parametrilor a i b ai modelului de regresie liniar unifactorial cu M.C.M.M.P.:</p> <p> relaia dintre r i parametrii modelului de regresie:</p> <p> raportul de corelaie:</p> <p>R2 - gradul de determinaie;</p> <p>- valori ajustate;</p> <p>- valori reale.5. SERII CRONOLOGICE: indicatori absolui: modificarea absolut:</p> <p> cu baz fix: </p> <p> cu baz n lan: </p> <p> valoarea absolut a unui procent de modificare:</p> <p> cu baz fix:</p> <p>, dac: </p> <p>dac: </p> <p> cu baz n lan:</p> <p>, dac:</p> <p>, dac: </p> <p> indicatori relativi:</p> <p> indicele (dinamica):</p> <p> cu baz fix: ,</p> <p> cu baz n lam: ,</p> <p> ritmul (rata, procent de modificare):</p> <p> cu baz fix: , </p> <p> cu baz n lan: , </p> <p> indicatori medii:</p> <p> media:</p> <p> pentru serii pe intervale:</p> <p> pentru serii de momente cu intervale egale ntre momente avem media cronologic simpl:</p> <p> pentru serii de momente cu intervale neegale ntre momente avem media cronologic ponderat:</p> <p> modificarea absolut medie:</p> <p> indicele mediu;</p> <p> ritmul mediu:</p> <p> ajustarea seriilor cronologice:</p> <p> metode mecanice:</p> <p> metoda modificrii absolute medii:</p> <p>; ;; </p> <p> metoda indicelui mediu:</p> <p>; ;; </p> <p> metode analitice:</p> <p> funcia liniar:</p> <p>Estimarea parametrilor a i b se face cu ajutorul M.C.M.M.P.</p> <p> unde: ( ;</p> <p>.Se renumeroteaz perioadele astfel nct .6. INDICI STATISTICI:</p> <p>unde:yi - fenomenul complex;</p> <p>Ex.:yi- valoarea;xi - factorul de tip calitativ;</p> <p>xi- preul;fi - factorul de tip cantitativ.</p> <p>fi-cantitatea. indici individuali:</p> <p>; </p> <p> indici de grup (agregai): pentru fenomenul complex: </p> <p> pentru factorul calitativ (indice de tip Paasche): </p> <p> pentru factorul cantitativ (indice de tip Laspeyres): </p> <p> Indici de grup calculai ca medie de indici individuali: pentru fenomenul complex:</p> <p>sau</p> <p> pentru factorul calitativ:</p> <p> pentru factorul cantitativ:</p> <p>Exemplificare pentru indicii valorii, volumului fizic i al preurilor:</p> <p>sau</p> <p> indici calculai ca raport a dou medii:</p> <p>;</p> <p>Ex.: </p> <p> ; </p> <p>unde: salariul mediu;</p> <p> productivitatea medie pe societate;</p> <p> productivitatea pe secii; structura numrului de muncitori.</p> <p> indice cu structur variabil:</p> <p> indice cu structur fix:</p> <p> indicele variaiei structurii:</p> <p> descompunerea geometric;</p> <p>descompunerea analitic.</p> <p>2544</p> <p>_1321019054.unknown</p> <p>_1321118820.unknown</p> <p>_1321128895.unknown</p> <p>_1321130153.unknown</p> <p>_1321170042.unknown</p> <p>_1321171724.unknown</p> <p>_1321172342.unknown</p> <p>_1321194875.unknown</p> <p>_1321172599.unknown</p> <p>_1321171984.unknown</p> <p>_1321170692.unknown</p> <p>_1321170864.unknown</p> <p>_1321170856.unknown</p> <p>_1321170088.unknown</p> <p>_1321170267.unknown</p> <p>_1321170098.unknown</p> <p>_1321170051.unknown</p> <p>_1321131367.unknown</p> <p>_1321166892.unknown</p> <p>_1321168106.unknown</p> <p>_1321169554.unknown</p> <p>_1321167911.unknown</p> <p>_1321167924.unknown</p> <p>_1321167598.unknown</p> <p>_1321132160.unknown</p> <p>_1321132185.unknown</p> <p>_1321132253.unknown</p> <p>_1321132177.unknown</p> <p>_1321131378.unknown</p> <p>_1321131312.unknown</p> <p>_1321131332.unknown</p> <p>_1321130164.unknown</p> <p>_1321129339.unknown</p> <p>_1321130046.unknown</p> 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