  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

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