Business Statistics Formulae

BUSINESS STATISTICS USEFUL FORMULAE 1. Sum of all deviations from mean

=0

2. Pie chart area

= 360o X relative frequency

3. Stregf’s formula for class interval

=

Range No. of classes

4. Range

= Difference between maximum & minimum

5. Class Interval (C.I.)

=

Range No. of classes

6. Mean 7.

=

f*x

f 

Median / Mean M = L + i/f {N/2 – C. F} L=

Lower Limited of median class interval. interval. To select L find our median class interval. The formula for median class interval is: (n+1)/2 – where n =

cumulative frequencies

i

= class interval

F

= Frequency of median class

C. F

= Cumulative Frequency of class preceding the median class

N

= Total No. of frequencies

8. (n1 +n2) * x12 = n1* x1 + n2* x2 9. Shortcut method to calculate mean: Actual mean = A +

f*d

*i

f  A

= Assumed Mean, can be any class interval / frequency

d i

= (x – A) C.I = C. I = Class Interval

The actual mean is independent of the assumed mean

n

10. Geometric Mean G. M =

x1, x2, x3, x4 ……xn

11. Growth factor @ given interest rate = principal + (interest / 100) n

12. New Principal Pn = Po (1 + r) or log Pn = log Po + n log (1+r) Pn = New Principal Po = Original Principal r = rate of interest n = no. of years n 13.

Harmonic Mean 1/H.M = X

i/x 1

x

n Or H.M. =

x

i/x X

1

H.M. is used to calculate growth where the growth rate is negative 14.

Mode = L + i * [(F1 – Fo) / (2F1 – Fo – F2)] L=

Lower limit of the modal class interval. Modal class interval is the class interval with the highest frequency

i=

Class interval

Fo = Frequency of class preceding the modal class F1 = Frequency of the modal class F2 = Frequency of class succeeding the modal class 15.

Quartile / Decile / percentile: Quartile = k [(n+1)/4] k = nth position of the quartile n = cumulative frequency For

Ist quartile k = 1 IInd quartile k = 2 IIIrd quartlie k = 3

Decile = k [(n+1)/10] Percentile = k [(n+1)/100] 16.

For Grouped Data: Q = L + i/F ((kN/4) – CF)

Q L

= =

i

=

F

=

Quartile Lower limit of the modal class interval. Modal class interval is the class interval with the highest frequency Class interval Frequency of the modal class nth position of the quartile Cumulative Frequency of the class Total No. of frequencies

k = C. F. = N =

17.

Quartile Deviation – (Q3 – Q1) / 2

18.

Coefficient of Quartile Deviation : (Q 3 – Q1) / (Q3 + Q1)

19.

Mean absolute Deviation =

20.

Variance of data = Or S.D. =

21.

xi - x N 2

(xi – x )

variance

or

xi - x n

n 2

=

(xi – x )

n

Range = Difference between the highest and the lowest values. SD – takes all values in the distribution & range does not give information on the complete data set.

22. 23.

24.

2

(xi – x )

2 2

n

=

2

= 2

f*d

f & x

=A+

2

where d = xi – A

i

f  f*x f 

25.

2

( x )

f 

f (xi - x )

=fd

2

(xi) n

Coefficient of variation = 100 * X

& A = Assumed Mean