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1、商务统计公式总结l l l l l 2Sample mean X=1nnQ1 at (n+1)/4 Q2 at (n+1)/2 (the median position) Q3 at 3(n+1)/4 Interquartile range = Q3 Q1 Xi=1niX+X+L+Xnl Sample variance S=2(Xi=1ni-X)2n-1n(X1-X)2+(X2-X)2+.+(Xn-X)2=n-1l Sample standard deviation s=2(X-X)ii=1n-1SCV=l Coefficient of Variation Xl Z Score Z=100%
2、X-X Sl Population mean m=Xi=1NiNN=X1+X2+L+XNN-)2Nl Population variance =2(Xi=1iNl Population standard deviation =(X-)ii=12Nl Chebyshev Rule: at least (1 - 1/k2) x 100% of the values will fall within k l P(A or B) = P(A) + P(B) - P(A and B) l P(A|B)=P(AandB)P(B)l Two events are independent if and onl
3、y if: P(A|B)=P(A) l l P(A andB)=P(A|B)P(B) P(A andB)=P(A)P(B) (If A and B are independent) l select X objects from n objects: nCx=n! (number of different ways) X!(n-X)!l select and arrange: nPx=n!(n-X)!l Expected Value ( mean) (discrete distribution) m = E(X) = XiP(Xi)=X1P(X1)+X2P(X2)+XnP(Xn) i=1Nl
4、Variance of a discrete random variable =2X-E(X)P(X) 2iii=1Nl Standard Deviation of a discrete random variable = =2X-E(X)P(X)2iii=1Nxn-xP(X)=nCxp (X successes in n trials) Binomial Distribution Mean =E(x)=np Variance 2=np(1-p) Standard Deviation =np(1-p) Discrete Probability Distributions e-llx P(X)=
5、 (l=expected number of events;e = 2.71828.) X! Poisson Distribution Mean = Variance = Standard Deviation = Standardized Normal Distribution translation Z= 2X- X= of the Mean X (is normal if population is normal or n 30) Sampling Distributions of the Proportion (normal distribution if X=nZ=(X-X)X=(X-
6、)np=p=(1-)nn5 and n(1-)5) p-pp-pZ= pp(1-p) n is Known XZnfor the Population Mean, Confidence Intervals is Unknown SXtn-1 nConfidence Intervals for p(1-p)the Population Proportion, pZn Z22 for mean e=Zn=ne2 Determining Sample Size 2(1-)(1- for proportion ) Z n= 2 e=Ze n can be estimated with a pilot sample (or conservatively use = 0.5)
