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PraveenKumar Keskar, profile picture
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Statistics formulae

This document provides formulas for various statistical measures including: 1) Measures of central tendency such as mean, median, and mode. 2) Measures of dispersion like range, quartile deviation, mean deviation, and standard deviation. 3) Probability formulas for additional theorem, conditional probability, Bayes' theorem, binomial distribution, and Poisson distribution. 4) Correlation coefficients including Pearson's and Spearman's methods. 5) Regression equations and time series analysis methods. 6) Formulas for index numbers including weighted and unweighted average, aggregative, and price index numbers.

STATISTICS FORMULAE MEASURES OF CENTRAL TENDENCY: 1) Range = Highest Value – Lowest Value 2) No. Of Class Intervals = 1+ 3.2 log N (Struge’s Rule) 3) Class Width = Range / No. Of Class Intervals. OR Class Intervals = Range / Class Width 4) Arithmetic Mean = ∑ ‫/ ݔ‬n, OR ∑݂‫ / ݔ‬N ొ ି ୔.େ.୊ L+ቈ ቉×H ୬ାଵ మ ଶ ୊ 5) Median = or Where: L = Lower limit of median class, PCF = Previous Cumulative Frequency, F= Frequency of the Median Class, & H= Width of the CI ‫+ܮ‬ቂ ቃ×ℎ ௙ଵି௙଴ ଶሺ௙ଵሻି௙௢ି௙ଶ 6) Mode = Where: Where: L = Lower limit of modal class, f1 = Highest Frequency in the Distribution, f0 = Preceding Frequency to the Highest Frequency in the Distribution, f2 = Succeeding Frequency to the Highest Frequency in the Distribution, & H= Width of the CI ௡ ୒ భ ౜ ∑ ∑ 7) Harmonic Mean = or ೣ ౮ ∑ ௅௢௚ ௫ ∑ ௙௅௢௚ ௫ 8) Geometric Mean = ‫݃݋݈݅ݐ݊ܣ‬ ‫݃݋݈݅ݐ݊ܣ‬ ௡ ே or PraveenKumar Keskar 1
ಿ ௥ቀ ర ቁି௉.஼.ி ‫ݎ‬ቀ ቁ ‫ݎ‬ቀ ቁ ݈+ቈ ቉×ℎ ௡ାଵ ேାଵ ସ ସ ி 9) Quartiles = or or ݊+1 ܰ+1 ‫ݎ‬ቀ ቁ or ‫ݎ‬ቀ ቁ 10 10 10) Deciles = or ಿ ௥ቀ ቁି௉.஼.ி ݈+ቈ భబ ቉×ℎ ி ‫ ݎ‬ቀ ଵ଴଴ ቁ ‫ ݎ‬ቀ ଵ଴଴ ቁ ௡ାଵ ேାଵ 11) Percentile = or or ಿ ௥ቀ ቁି௉.஼.ி ݈+ቈ భబబ ி ቉×ℎ MEASURES OF DISPERSION: 12) Range = Highest Value – Lowest Value ୌ୧୥୦ୣୱ୲ ୚ୟ୪୳ୣ – ୐୭୵ୣୱ୲ ୚ୟ୪୳ୣ ୌ୧୥୦ୣୱ୲ ୚ୟ୪୳ୣା ୐୭୵ୣୱ୲ ୚ୟ୪୳ୣ Co-efficient of Range = ୕ଷିொଵ ଶ 13) Quartile Deviation = ୕ଷିொଵ ொଷାொଵ Co-efficient of Q.D = ഥ ∑ |௫ି௫| ഥ ∑ ௙|௫ି௫| ௡ ே 14) Mean Deviation = or ெ௘௔௡ ஽௘௩௜௔௧௜௢௡ ௙௥௢௠ ௠௘௔௡ ெ௘௔௡ Co-efficient of MD = PraveenKumar Keskar 2
Standard Deviation = ට ට ∑ሺ௫ି௫̅ ሻమ ∑ ௙ሺ௫ି௫̅ ሻమ ௡ ே 15) or OR ∑x ଶ ∑ fx ଶ ට ∑ x2 −ቀ nቁ ට ∑ fx2 −ቀ ቁ n ୒ ୒ or × 100 ஢ ത ୶ Co-efficient of Variation = PROBABILITY: 16) Additional Theorem = PሺA ⋃ Bሻ = PሺAሻ + PሺBሻ − PሺA ⋂ Bሻ P ቆBൗAቇ = ୔ሺ୅ ⋂ ୆ሻ ୔ሺ୅ሻ 17) Conditional Theorem = ୔ሺ୅ሻ×୔ሺ୅ Baye’s Theorem = P ൬Aൗ ൰ = ൗ୉ ሻ Eଵ భ 18) ୅ൗ ሻ ∑ ୔ሺ୉భ ሻ×୔ሺ ୉ భ 19) Binomial Distribution: Probability Mass Function (P.M.F) = nେ౮ × ሺpሻ୶ × ሺqሻ୬ି୶ Where, ‫ݔ‬ = 0, 1, 2 _ _ _ n, p+q = 1 20) Poison Distribution ሺ௘ ష೘ ሻ×ሺ௠ሻೣ ௫! P.M.F = Where, x = 0, 1, 2, 3 _ _ _ _ _ _ _ _ ∞ PraveenKumar Keskar 3
௫ି௠ ఙ 21) Normal Distribution = Where m = mean & ߪ = Standard Deviation CORRELATION: 22) Karl Pearson’s Coefficient of Correlation: ௡ஊ௫௬ିሺஊ௫ሻሺஊ୷ሻ ඥ௡ஊ௫ మష ሺஊ௫ሻమ ඥ௡ஊ୷మష ሺஊ୷ሻమ r= 23) Spearman’s Rank Correlation: ଺ሺஊୈమ ሻ r = 1- [௡ሺ௡ ିଵሻ] మ where D = R1 – R2 If any rank is repeated then; ଺ሺஊୈమ ା େ.୊.ሻ r=1– [ ௡ሺ௡మ ିଵሻ ] ௠ሺ௠మ ିଵሻ ଵଶ C.F. = Where, m = No. of times the rank is repeated REGRESSION: 24) If X is dependent on Y= ത) (‫ = ) ̅ݔ- ݔ‬bxy (‫ݕ- ݕ‬ ఙ௫ ఙ௬ bxy = r 25) If Y is dependent on X = PraveenKumar Keskar 4
ത) (y - ‫ = ݕ‬byx (‫) ̅ݔ- ݔ‬ ఙ௬ ఙ௫ byx = r ௡ஊ୶୷ିሺஊ୶ሻሺஊ୷ሻ ௡ሺஊ୶మ ሻ ି ሺஊ୶ሻమ byx = ௡ஊ୶୷ିሺஊ୶ሻሺஊ୷ሻ ௡ሺஊ୷మ ሻି ሺஊ୷ሻమ bxy = r = ඥܾ௫௬ × ܾ௬௫ TIME SERIES 26) Method of Moving Averages 27) Method of Least Squares a) Linear Equation: y = a + bx ∑௬ ∑ ௫௬ ௡ ∑ ௫మ Where, a = ; b= b) Quadratic Equation: y = a + bx + cx2 Normal Equations are: Σy = na + bΣx + cΣx2 Σxy = aΣx + bΣx2 + cΣx3 Σx2y = aΣx2 + bΣx3 + cΣx4 INDEX NUMBERS 28) Unweighted Simple Average: a) Unweighted Arithmetic Mean Index Numbers = ஊ௉ ௡ P01 = PraveenKumar Keskar 5
b) Unweighted Geometric Mean Index Number = ஊ୪୭୥୔ ௡ P01 = Antilog ( ) 29) Unweighted Simple Aggregative Index Numbers = ஊ୔భ ஊ୔బ P01 = × 100 30) Weighted Average Relative Index Numbers: a) Weighted Arithmetic Mean Index Number = ஊ୛୔ ஊ୛ P01 = b) Weighted Geometric Mean Index Number = P01 = Antilog (ஊ୛୪୭୥୔) ஊ୛ 31) Weighted Aggregative Index Number = a) Laspeyre’s Price Index Number = ஊ୔భ ୕బ ஊ୔బ ୕బ P01 = × 100 b) Paasche’s Price Index Number = ஊ୔భ ୕భ ஊ୔బ ୕భ P01 = × 100 c) Marshall Edgeworth’s Price Index Number = ஊ୔భ ୕బ ା ஊ୔భ ୕భ ஊ୔బ ୕బ ା ஊ୔బ ୕భ P01 = × 100 d) Fisher’s Price Index Number = P01 = ඥP଴ଵ ሺLaspeyre′sሻ × P଴ଵ ሺPaasche′sሻ = ඨΣP1 Q0 × ΣP1 Q1 ΣP Q ΣP Q 0 0 0 1 PraveenKumar Keskar 6