Formulae Sheet MTH222

(forms part of the Examination answer book and the students are allowed to use it during the final Exam)

WARNING: This is an interim version to be worked on. The X-with-a-bar symbol is not properly shown on screen!
Your printed syllabus comprises a copy free of any errors!



Arithmetic Mean

Raw dataGrouped data
x = Sx
        n
x = Sfx
        n

Formula View



Variance

Raw dataGrouped data
S2= S(x-x)2 = Sx2 - n(x)2
         n                 n
S2 = Sf(x-x)2 = Sfx2 - n(x)2
                n                          n



Price Indices

Laspeyre Price IndexPaasche Price Index
L = Spnqo       x 100
          Spoqo
P = Spnqn       x 100
      Spoqn



Correlation Coefficients

Pearsons (Product Moment) CoefficientSpearman (Rank) Correlation Coefficient
r =       nSxy - Sx Sy
         Ö[ n Sx2 - (Sx)2 ] [ n Sy2 - (Sy)2 ]
Rs = 1 - 6Sd2
                 n(n2-1)



Probability

General Addition RuleGeneral Multiplication Rule
P(A or B) = P(A) + P(B) - P(A and B)P(A and B) =P(A) P(B|A)



Binomial Distribution

Binomial FormulaBinomial Coefficient
P(x) = nCx px (1-p)n-x nCx =       n!      
                  x! (n-x)!

m = np, s2 = np(1-p)


Conversion formula for Normal Distribution

z = x - m
s



The 95% confidence interval for the population mean

m=       x       ±       1.96 s
                              Ö
n


Test statistic for hypothesis tests on population mean

z =       x - m
            s /Ö n



Chi-squared test

c 2 = S(o-e)2
      e

with (r-1)(c-1) degrees of freedom