सांख्यिकी - सूत्र

नीचे दिए गए आँकड़े सूत्र की सूची में इस्तेमाल किया जाता है। प्रत्येक सूत्र एक वेब पेज से जुड़ा होता है जो सूत्र का उपयोग करने का वर्णन करता है।

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Chebyshev's Theorem - $ {1- \ _ frac {1} {k ^ 2}} $
Circular Permutation - $ {P_n = (n-1)!} $
Cohen's kappa coefficient - $ {k = \ frac {p_0 - p_e} {1-p_e} = 1 - \ frac {1-p_o} {1-p_e}} $
Combination - $ {C (n, r) = \ frac {n!} {R! (Nr)!}} $
Combination with replacement - $ {^ nC_r = \ frac {(n + r-1)!} {r! (n-1)!}} $
Continuous Uniform Distribution - f (x) = $ \ start {case} 1 / (ba), और \ text {जब $ a \ le x \ le b $} \\ 0, & \ text {जब $ x \ lt $ a या $ x \ gt b $} \ end {मामले} $
Coefficient of Variation - $ {CV = \ frac {\ sigma} {X} \ गुना 100} $
Correlation Co-efficient - $ {r = \ frac {N \ sum xy - (\ sum x) (\ sum y)} {\ sqrt {[N \ sum x ^ 2 - ((sum x) ^ 2] [N \ sum y ^ 2 - (\ योग y) ^ 2]}}} $
Cumulative Poisson Distribution - $ {F (x, \ lambda) = \ sum_ {k = 0} ^ x \ frac {e ^ {- \ lambda} \ lambda ^ x} {k!}} $

Deciles Statistics- $ {D_i = l + \ frac {h} {f} (\ frac {iN} {10} - c); i = 1,2,3 ..., 9} $
Deciles Statistics- $ {D_i = l + \ frac {h} {f} (\ frac {iN} {10} - c); i = 1,2,3 ..., 9} $

Harmonic Mean - $ HM = \ frac {W} {\ sum (\ frac {W} {X})} $
Harmonic Mean - $ HM = \ frac {W} {\ sum (\ frac {W} {X})} $
Hypergeometric Distribution - $ {h (x; N, n, K) = \ frac {[C (k, x)] [C (Nk, nx)]} {C (N, n)}} $

Interval Estimation - $ {\ mu = \ bar x \ pm Z _ {\ frac {\ अल्फा} {2}} \ frac {\ sigma} {\ sqrt n}} $

Logistic Regression - $ {\ pi (x) = \ frac {e ^ {\ Alpha + \ Beta x}} {1 + e ^ {\ Alpha + \ beta x}}} $

Mean Deviation - $ {MD} = \ frac {1} {N} \ sum {| XA |} = \ frac \ \ sum {| D |}} {N} $
Mean Difference - $ {माध्य \ _ अंतर = \ frac {\ _ x_1} {n} - \ frac {\ _ x_2} {{}} $
Multinomial Distribution - $ {P_r = \ frac {n!} {(N_1!) (N_2!) ... (n_x!)} {P_1} ^ {n_1} {P_2} ^ {n_2} ... {P_x} ^ {! n_x}} $

Negative Binomial Distribution - $ {f (x) = P (X = x) = (x-1r-1) (1-p) x-rpr} $
Normal Distribution - $ {y = \ frac {1} {\ sqrt {2 \ pi}} e ^ {\ frac {- (x - \ mu) ^ 2} {2 \ "सिग्मा}}} $

One Proportion Z Test - $ {z = \ frac {\ hat p -p_o} {\ sqrt {\ frac {p_o (1-p_o)} {n}}} $

Permutation - $ {{^ nP_r = \ frac {n!} {(nr)!}} $
Permutation with Replacement - $ {^ nP_r = n ^ r} $
Poisson Distribution - $ {P (Xx)} = {e ^ {- m}}। \ Frac {m ^ x} {x} $!
probability - $ {P (A) = \ frac {\ _ के अनुकूल / मामलों की संख्या {{कुल मिलाकर \ _ \ _ \ _ के समान रूप से होने की संभावनाएँ = = \ frac {m} {n}} $
Probability Additive Theorem - $ {P (A \ or \ B) = P (A) + P (B) \\ [7pt] P (A \ cup B) = P (A) + P (B)} $
Probability Multiplicative Theorem - $ {P (A \ and \ B) = P (A) \ टाइम्स P (B) \\ []pt] P (AB) = P (A) \ टाइम्स P (B)} $
Probability Bayes Theorem - $ {P (A_i / B) = \ frac {P (A_i) \ टाइम्स P (B / A_i)} {\ sum_ {i = 1} ^ k P (A_i) \ टाइम्स P (B / a_i)}} $
Probability Density Function - $ {P (a \ le X \ le b) = \ int_a ^ bf (x) d_x} $

Reliability Coefficient - $ {विश्वसनीयता \ गुणांक, \ RC = (\ frac {N} {(N-१)}) \ टाइम्स (\ frac {(कुल \ _ Variance \ - Sum \ of \ Variance)} {कुल भिन्नता}} $
Residual Sum of Squares - $ {RSS = \ sum_ {i = 0} ^ n (\ epsilon_i) ^ 2 = \ sum_ {i = 0} ^ n (y_i - (\ Alpha + \ beta x_i)) ^ 2} $}

Shannon Wiener Diversity Index - $ {H = \ sum [(p_i) \ टाइम्स ln (p_i)]} $
Standard Deviation - $ \ sigma = \ sqrt {\ frac {\ _ sum_ {i = 1} ^ n {(x- \ bar x) ^ 2}} {N-1}} $
Standard Error ( SE ) - $ SE_ \ बार {x} = \ frac {s} {\ sqrt {n}} $
Sum of Square - $ {\ _ \ _ का वर्ग \ _ \ _ \ _ \ _ (x_i - \ bar x) ^ 2} $