Statistics Formulas ppt

Submitted by Harjeet Singh
MBA- I semester

1. Business Statistics Formula’s Submitted By :- Harjeet Singh MBA – I Semester Baddi University Emerging Technology & Science

2. Formula Individual Series Discrete Series Continuous Series Direct _ ∑X X = ----- N _ ∑fX X = ----- N _ ∑fm X = ------ N Short cut _ ∑d X = A + ----- N _ ∑fd X = A + ----- N _ ∑fd X = A + ----- N Step Deviation _ ∑fd X = A + ----- * i N _ (d= X - X) _ ∑fd X = A + ----- * i N _ (d= X - X) M ean

3. Mean Correcting Incorrect Mean Average Mean Correct ∑X = Incorrect ∑ X – Wrong Item + Correct Item _ Correct ∑X Correct X = ---------------- N Combined Average Mean:- _ _ _ N 1 X 1 + N 2 X 2 X = ----------------- N 1 + N 2 Weighted Average Mean:- _ ∑WX X = -------- ∑W

4. Individual Series Discrete Series Continuous Series N+1 Size of --------- th item 2 N+1 Size of --------- th item 2 { N/2 – Cf} L 1 + ------------ * i f (Size of N/2 th item) Median

5. Computing of Quartiles Individual & Discrete Series Continuous series N + 1 Q 1 = Size of -------- th item 4 3(N + 1) Q 3 =Size of ----------- th item 4 Q 3 - Q 1 QD = ---------- 2 N Q 1 = Size of ---- th item 4 3(N) Q 3 = Size of ------- th item 4 QD = { N/4 – Cf} L 1 + ------------ * i f Q 3 - Q 1 QD Coeff. = ----------- Q 3 + Q 1

6. Individual series :- 60(N + 1) P 60 = Size of ------------ th item 100 Continuous Series :- 50(N) P 50 = Size of --------- th item 100 P = { N/100 – Cf} L 1 + ------------ * i f Computing of Percentiles

7. f 1 – f Z = L 1 + ------------ * i 2 f 1 – f – f 2 Z = 3*median – 2*mean Mode

8. 1 ) Range :- L – S L – S Coeff. :- --------- L + S 2) Quartile Deviation :- Individual & Discrete Series :- Q 3 - Q 1 / 2 Continues series :- Q 3 - Q 1 / 2 Q 3 - Q 1 Coeff . = ----------- Q 3 + Q 1 Dispersion

9. 3) Mean Deviation :- ∑|d| Individual Series = -------- N ∑ f |d| Discrete & Continues Series = --------- N Mean Deviation Coeff. = ----------------------- Median

10. 4) Standard Deviation :- Individual Series:- _______ Actual Mean (σ) = ⎷ ∑ x 2 / N ________________ Assumed Mean (σ) = ⎷ ∑d 2 /N - (∑d / N) 2 Discrete Series:- ________ Actual Mean (σ) = ⎷ ∑ fx 2 / N _______________ Assumed Mean (σ) = ⎷ ∑ fd 2 /N - (∑fd / N ) 2 ________________ Continues Series (σ) = ⎷ ∑ fd 2 /N - (∑fd / N ) 2 * i

11. _ _ _ N 1 X 1 + N 2 X 2 5) Combined Mean X 12 = ------------------ N 1 + N 2 6) Combined Standard Deviation :- ________________________________________ | N 1 σ 1 2 + N 2 σ 2 2 + N 3 σ 3 2 + N 1 d 1 2 + N 2 d 2 2 + N 3 d 3 2 (σ) =⎷ ----------------------------------------------------------------- N 1 + N 2 + N 3 _ _ _ _ d1 = |X1 - X123| d2 = |X2 - X123| _ _ d3 = |X3 - X123| _ Coefficient of Variance = σ / X * 100

12. Karl Pearson's Skewness :- SK P = Mean – Mode / Standard Deviation 2) Bowley’s Skewness :- SK B = Q 3 + Q 1 – 2 Median / Q 3 - Q 1 3) Kelly’s Skewness :- SK K = P 10 + P 90 – 2 Median / P 9 - P 10 Skewness

13. 1) Laspayer’s Method P 01 = ∑p 1 q / ∑p q * 100 2) Paasch’s Method P 01 = ∑p 1 q 1 / ∑p q 1 * 100 3) Bowley’s Method = Laspayer’s + Paasch’s / 2 ___________________ 4) Fisher’s Method = ⎷ Laspayer’s * Paasch’s 5) Marshal Method = ∑p 1 q + ∑p 1 q 1 / ∑p q + ∑p q 1 * 100 6) Kelly ‘s Method = p 1 q / p 1 q *100 Index Number

14. Time reversal Test :- P 01 * P 10 = 1 Factor Reversal Test:- p 01 * q 01 = ∑p 1 q 1 / ∑p q Weighted Average Relative Method:- P 01 = ∑pv / ∑v = ∑p 1 / ∑p * 100 (P = Price Relative )

15. Actual Mean :- ∑ xy ∑xy r = --------- or ------------ N σx σy ⎷ ∑ x 2 * ∑ y 2 Assumed Mean :- N ∑dx dy - ∑dx * ∑dy r = --------------------------------- ⎷ N ∑dx 2 - (∑dx) 2 * ⎷ N ∑dy 2 - (∑dy) 2 Karl Pearson’s Correlative Co-efficient

16. Regression Equation of (X on Y) :- _ σy _ (X – X) = r ------ (Y - Y) σx σx N ∑dx dy - ∑dx * ∑dy r------ = ------------------ σy ⎷ N ∑dy 2 - (∑dy) 2 Regression

17. 2) Regression Equation of (Y on X) :- _ σy _ (Y – Y) = r ------ (X - X) σx σy N ∑dx dy - ∑dx * ∑dy r------ = -------------------- σx ⎷ N ∑dx 2 - (∑dx) 2 _ ∑x _ ∑y X = ------ ; Y = ------ N N

18. Regression Coefficient :- r = ⎷bxy * byx Time Series:- Yc = a + bx a = ∑y / n b = ∑xy / ∑x 2