STA301 Formulas and Definitions Lectures 1-45

Average Speed:

Total Distance Travelled Average Speed Total Time Taken

Distance Time = Speed

Distance Speed = Time

Distance = Speed Time

Mode:

1)

1) 2) fm f X l h fm f fm f

Empirical Relation between Mean, Median and Mode:

Mode Median Mean

Range:

m Range X X

Mid-Range:

X Mid Range = m X

Mid Quatile Range:

Mid Range = Q Q

Coefficient of Dispersion:

Coefficient of Dispersion = m

m X X

X X

Geometric Mean:

log log X G M anti n

log log f X G M anti f

Equation of a Straight Line · Y · a · bX · Standard Error of Estimate:

yx Y a Y b XY s n

Normal Equations:

Y na b X

XY a X b X

Correlation: · X · X · Y · Y r · X · X · Y · Y · PEARSON’S COEFFICIENT OF CORRELATION

XY X Y n r X X n Y Y n

Linear Correlation of Coefficient:

n xy x y r n x x n y y

Regression Line of Y on X:

n xy x y byx n x x

Division of Circle:

Cell Frequency

Total Frequency

Binomial Coefficient:(

n r

C

n n n r r

r n a b a b r

Probability Formula:

m = P(A) = n

No. of Favourable Outcomes = P(A) = Total No. of Possible Outcomes

Mutually Exclusive Events:

If A and B mutually exclusive events,

P(A B) = P(A) + P(B)

Complementation Law of Probability:

P(A) = 1 P A

Addition Law:

P(A B) = ( ) P A P B P A B

Conditional Probability:

P(A B) P(A/B) = P(B)

P(A B) P(B/A) = P(A)

Multiplication Law:

P(A ) = P(A)P(B/A) B

Baye’s Theorem:

(A P A P B A P B P A P B A P A P B A

Computation of Standard Deviation Probability Distribution:

As we know, X P X XP X S D X P X P X

S D X X P X XP X

P X

Coefficient of Variation: · σ · µ