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![maths - Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X"-1 f(x) = Ixll "(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X"-1 f(x) = Ixll "(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_294809_37306972_1772681288903_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=903_sc.jpg "maths - Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X\"-1 f(x) = Ixll \"(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X Complete Formulas Functions] 1, FUNCTION २. DOMAIN CODOMAIN & RANGE DEFINITION Domain > Sef of all possible inpufs A funcfion f from sef A to set Bl Set of all possible outputs rule that assigns each element is Codomain > exacfly one elemenf of 8. Sef of acfual oufpufs of A Range _ Range = Codomain Writren as: f:A-8 If x ٤ A Then f(x) & B TYPES OF FUNCTIONS 4 (a) One-One Function (Injective): f(x1) = f(x2) => X1 = X2 ३. REPRESENTATION OF FUNCTIONS Set of ordered pairs b) Many-One Funcfion: Two or more Arrow diagram] elements of domain have the same Graph image. Algebraic expression] (c) Onto Function (Surjective): 5. ALGEBRAIC FUNCTIONS Range Codomain] d) Info Funcfion : Range C Codomain (a) Constant Function: f(x) = c (e) Bijective Function: One-one and onto (b) Constant Function: f(x) = c function (b) Identity Function: f(x) = X (c) Polynomial Function: 6. MODULUS FUNCTION f(x) + ٠٠٠ + 00 anxn ৭n-1X\"-1 f(x) = Ixll \"(X) (d) Rationdl Function: F(x) = Ixl = X X>0 q(x)+0 Ixl =-xl X < 0 7. GREATEST INTEGER FUNCTION 8 COMPOSITION OF FUNCTIONS f(x) = [x] If f : A -> B ond g : B -> C greatest integer < x [x] (g ৭ f)(x) g(f(x)) Example: [2.7] = 2, [-1.3] =-2 10. GRAPH OF FUNCTIONS 9. INVERSE FUNCTION A function f has an inverse if and Straight line] Linear funcfion ) f is bijecfive only if Quadraric function Parabola If f(x) then f-1(y) = * Horizonfql line' ٧ Constant function Property: f(f-1(x)) = X , f-1(f(x)) = X - ShareChat")
![maths - Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_293606_2f88db3a_1772507292452_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=452_sc.jpg "maths - Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf - ShareChat")
![maths - Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_956284_1cb90884_1772443275863_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=863_sc.jpg "maths - Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf Starisrics Complefe Formulas 1. Mean (Arithmetic Mean) 2. Median (a) Individual Series () Individudl Series Ex n+lth observation] Mean Median 2 (b) Discrete Series (b) Discrete Series Efx Value corresponding 1o Median Mean Zf 2 cumuldtive frequency 2 (c) Continuous Series Direct Method (c) Continuous Series Efx Mean [(ڈ-4)]xh Zf Median + (d) Assumed Mean Method] ऋ = a + (Efd 1 = lower limit of median class] Where: Zf frequency before cf = cumulafive Where: d = _ 0 median class Step (e) Deviation Method f = frequency of median class Zfd` h = clqss width Xh x =a + Zf Q Where: d = 4. Empirical Relation Mode = 3 Median २ Mean 3. Mode (a) Discrete Individual Series frequency of modal class f1 frequently Value occurring Mode frequency of preceeding class most fo frequency of succeeding class (b) Continuous Series f2 fol Mode = [ + Xh 2f1 fo - f2 6. Standard Deviation] Sfandard Deviafion (o) = V Variance 5. Variance] V02 () Individudl Series E( 7. Coefficient of Variation (CV) 02 డ (b) Discrete Series CV = X 100 Ef( ~) 02 ٤f 8. Comparison of Two Data Sets Step Deviation Method (c) Gredter CV = Gredter varidbility [Zfd2 Efal X h२ 02 consisfency Smaller CV = More Zf Zf - ShareChat")