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Statistics formula43[1]
- 1. STATISTICS FORMULA Ankit Chauhan 17PBA006 Baddi University of emerging sciences and technology
- 2. Measure of central tedendancy Median Mean Mode
- 3. Mean Formula Individual Discrete Continuous DIRECT 𝛴𝑋 𝑁 𝛴𝑓𝑋 𝑁 𝛴𝑓𝑚 𝑁 SHORT CUT A+ 𝛴𝑑 𝑁 A+ 𝛴𝑓𝑑 𝑁 A+ 𝛴𝑓𝑑 𝑁 STEP DEVIATION A+ 𝛴𝑓𝑑′ 𝑁 ∗ 𝑖 A+ 𝛴𝑓𝑑 𝑁 ∗ i (d=X-X͞ )
- 4. Mean COMBINED MEAN 𝑵 𝟏X͞ 𝟏+𝑵 𝟐X͞ 𝟐 𝑵𝟏+𝑵𝟐 , WEIGHTED MEAN ∑𝑾𝑿 ∑𝑾
- 5. Median Individual N+1/2 (when in points add L+U/2) Continuous M= L+ 𝑁 2 −𝑐𝑓 𝑓 ∗ 𝑖
- 7. Measure of dispersion Quartile deviation Mean deviation Standard deviation
- 8. QUARTILE DEVIATION Individual Continuous Q1= 𝑁+1 4 Q3= 3 𝑁+1 4 QD= 𝑄3−𝑄1 2 , QD=𝐿 + 𝑁 4 −𝑐𝑓 𝑓 ∗ 𝑖 Coeff. = 𝑄3−𝑄1 𝑄3+𝑄1
- 9. STANDARD DEVIATION DIRECT SHORT CUT STEP DEVIATION Individual =SD= 𝚺𝐗 𝟐 𝐍 OR 𝚺(𝐗−𝐗͞ 𝐍 𝚺𝐝𝐱 𝟐 𝐍 − ( 𝚺𝐝𝐱 𝐍 )² = 𝚺𝐝𝐱 𝟐 𝐍 − ( 𝚺𝐝𝐱 𝐍 )² ∗ 𝐂 Discrete & continuous 𝚺𝐟𝐝𝐱² 𝐍 − ( 𝚺𝐟𝐝𝐱 𝐍 )² 𝚺𝐝𝐱′ 𝟐 𝐍 − ( 𝚺𝐝𝐱′ 𝐍 )² ∗ 𝐂 dx’= 𝐝𝐱 𝐂
- 10. STANDARD DEVIATION Coefficient of SD= ϭ 𝑋 AND Coefficient of variation or C.V = ϭ 𝑋 ∗ 100 Combined SD= 𝑵 𝟏ϭ 𝟏+𝑵 𝟐ϭ 𝟐+𝑵 𝟏 𝒅 𝟏+𝑵₂𝒅₂ 𝑵 𝟏+𝑵₂
- 11. MEAN DEVIATION Individual Discrete & CONTINOUS COFFICENT MD= 𝛴│𝑑 𝑁 MD= 𝛴𝑓│𝑑│ 𝑁 𝑀𝐷 𝑀𝐸𝐷𝐼𝐴N 𝑂𝑅 𝑀𝐸𝐴𝑁
- 12. SKEWNESS Karl pearson Bowleey Kelly 𝐦𝐞𝐚𝐧 − 𝐦𝐨𝐝𝐞 𝑺𝑫 𝑸𝟑 + 𝑸𝟏 − 𝟐 𝑴𝑬𝑫𝑰𝑨𝑵 𝑸𝟑 − 𝑸𝟏 𝒅𝟗 + 𝒅𝟏 − 𝟐𝒎𝒆𝒅 𝒅𝟗 − 𝒅𝟏
- 13. Weighted aggregative Methods Formula Price Quantity Laspeyre’s Σp1q0 Σp0q0 ∗ 100 Σq1p0 Σq0p0 ∗ 100 Paaschee’s Σp1q1 Σp0q1 ∗ 100 Σq1p1 Σq0p1 ∗ 100 Fisher’s Σp1q0 Σp0q0 ∗ Σp1q1 Σp0q1 ∗ 100 Σq1p0 Σq0p0 ∗ Σq1p1 Σq0p1 ∗ 100 Dorbish & Bowley’s Σp1q0 Σp0q0 + Σp1q1 Σp0q1 ∗ 100 2 Σq1p0 Σq0p0 + Σq1p1 Σq0p1 ∗ 100 2 Marshall edgeworth’s Σp1q0 + Σp1q1 p0q0 + p0q1 ∗ 100 Σq1q0 + Σq1p1 Σq0p0 + Σq0p1 ∗ 100
- 14. INDEX NUMBERS Time Reversal Test : P01 X P10 = 1 Factor Reversal Test P01 XQ01 = ΣP1q1/ΣP0q0
- 15. CORELATION (Actual mean) Assumed mean) Actual data r= 𝛴𝑥𝑦 𝛴𝑥2.𝛴𝑦2 r= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦 𝑁𝛴𝑑𝑥²− 𝛴𝑑𝑥 2. 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)² r= 𝑁.𝛴𝑋𝑌−𝛴𝑋.𝛴𝑌 𝑁.𝛴𝑋²− 𝛴𝑋 2. 𝛴𝑌²−(𝛴𝑌)²
- 16. When ranks are not given
- 17. Rank are equal R = 1 − 6[∑𝐷2+ 1 12 (𝑚3−𝑚)+ 1 12 (𝑚3−𝑚) 𝑛3−𝑛
- 18. REGRESSION 1.Y on X Y=a+ bX ΣY=Na+bΣx ΣXY=aΣX+bΣX² 2.X on Y X=a+ bY ΣX=Na+bΣY ΣXY=aΣY+bΣY²
- 19. Equation using coefficient (Using Mean) 1.Y on X Y- X̅) byx= 𝑁.𝛴𝑥𝑦−𝛴𝑥.𝛴𝑦 𝑁.𝛴𝑥²−(𝛴𝑥)² 2.X on Y X-X̅=bxy(Y- bxy= 𝑁.𝛴𝑥𝑦−𝛴𝑦.𝛴𝑥 𝑁.𝛴𝑦²−(𝛴𝑦)²
- 20. Assumed mean 1.Y on X Y-Y̅=byx(X-X̅) byx= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦 𝑁.𝛴𝑑𝑥²−(𝛴𝑑𝑥)² 2. X on Y X-X̅=bxy(Y-Y̅) bxy= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑦.𝛴𝑑𝑥 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²
- 21. Time series Least square method YC = a +bx if x =0 then a = ∑y 𝑁 b = ∑xy ∑x²