# All Data-analysis Formulas List

## Vector Cross Product

#### Formula:

A x B = {(x,y) | x ε A ^ y ε B}

## Standard Error (SE)

#### Formula: Where,

SE = Standard Error
s = Standard Deviation
n = Size (Number of Observations) of the Sample.

## Coefficient of variance

#### Formula: Where,

Cv = Coefficient of Variation
σ = Standard Deviation
μ = Mean

## Percentage / Percent Error

#### Formula:

Percent Error = (observed value - True value)/True value)*100)

## Skewness

#### Formula: Where,

Xavg = Mean of Samples
Xi= The ith Sample
n = Number of Samples

## Possible Vowels Rearrangement

#### Formula:

Number of Arrangements = M! / N!
N! = N1! x N2! ...NM!

Where,

M! = Total number of vowel letters,
N! = Number of occurrences of each duplicate vowels.

## Skewness Coefficient

#### Formula:

Skewness Coefficient = 3 x (mean - median) / σ

Where,

σ=Standard deviation.

## Percentile Rank (PR) Statistics

#### Formula:

PR% = L + ( 0.5 x S ) / N

Where,

L = Number of below rank,
S = Number of same rank,
N = Total numbers.

## Cumulative Sum (CUSUM)

#### Formula: Where,

St = Average Run Length,
μ = Target Mean,
σ = Standard Deviation,
k = Reference value,
Ci+ = Upper Control Limit (UCL)
Ci- = Lower Control Limit (LCL)

## Mid and Semi Quartiles

#### Formula:

Mid Quartile = ( Third Quartile + First Quartile ) / 2
Semi Quartile = ( Third Quartile - First Quartile ) / 2

## Inter Quartile Range (IQR)

#### Formula:

InterQuartile Range (IQR) = Third Quartile - First Quartile.

## R-Squared (Coefficient of Determination)

#### Formula:

Correlation Coefficient ( r ) = N x ∑ XY - ( ∑ X ) ( ∑ Y ) / √ N x ( ∑ X2 - ( ∑ X )2 √ N x ( ∑ Y2 - ( ∑ Y )2

Coefficient of Determination ( r2 ) = r x r.

## Grade Point Average (GPA)

#### Formula:

Total Grades = Σ( Grade * Credit Hours )
GPA = Total Grades / Total Credit Hours

## Multiple Regression (MLR)

Formula Used:
Y = a + b1X1 + b2X2 + ... + bnXn

Where,
a - Y intercept point
b1, b2, ... , bn - Slope of X1, X2, ... , Xn respectively

## Bessel's Integral Function

#### Formula: Where,

Jn - First Kind Bessel Function

## Effect Size

#### Formula: Where,

d = Cohen's d Value (Standardized Mean Difference),
M1,M2 = Mean Values of the First and Second Dataset,
SD1,SD2 = Standard Deviation of the First and Second Dataset,
r = Effect Size.

## One Way ANOVA Matrix

Formula Used:
Sums of squares Formula Mean squares Formula F Formula ## Covariance

#### Formula:

Mean = Sum of Values Entered / N ## Regression Intercept Confidence Interval

Formula Used: Where,
β0 = Regression intercept
k = Number of Predictors
n = Sample Size
SEβ0 = Standard Error
α = Percentage of Confidence Interval
t = t-Value

## Cp and Cpk

#### Formula :  Where,

USL = Upper Specification Limit,
LSL = Lower Specification Limit.

## Post Hoc Power Statistical Analysis

Formula:
P = 2 x ( 1 - Φ(z) )

Where,

P = Post HOC Statistical Power Analysis
z = x̄ / σ√N
x̄ = Mean
σ = Standard Deviation
N = Number of Samples

## PP and PPK Index

Formula :  Where,

USL = Upper Specification Limit,
LSL = Lower Specification Limit.

## Comparative Error - Statistical Significance

#### Formula

Comparative Error = 1.96 x √ (r1(100-r1) Ã· s1) + (r2(100-r2) Ã· s2)

Where,

r1 = Percentage Response 1
r2 = Percentage Response 2
s1 = Sample Size 1
s2 = Sample Size 2

## Weak Law of Large Numbers

Formula: Where,

μ = Sample mean
n = Number of samples
Xi = Sample value

## Decile

Formula: Where,

Li = Lower limit of the decile class
N = Sum of the absolute frequency
Fi-1 = Absolute frequency lies below the decile class
ai = Width of the class containing the decile class

## Odds Ratio Confidence Interval

#### Formula:

Odds ratio = ( a / c ) / ( b / d )

Where,

a,b = Positive Test Values
c,d = Negative Test Values

## Ti 83 Exponential Regression Equation

#### Formula:

y = a x bx

Where,

The variables a and b denotes the coefficients of exponential equation.

## Harmonic Series Partial Sum

Formula :
Harmonic Series = 1 + 1/2 + 1/3 + 1/4 + ... (Overtone Method)

## Harmonic Number and Resonance Frequency

Formula:  ## Adjusted R Squared

Formula: ## Quartile Deviation

#### Formula :

QD = (Upper Quartile - Lower Quartile) / 2

## Cronbach's Alpha Reliability

Formula Used:
Reliability = N / ( N - 1)x(Total Variance - Sum of Variance for Each Question )/Total Variance
where,
N is no of questions,

## Outlier

Formula :
Outlier datas are, < Q1 - 1.5xIQR (or) > Q3 + 1.5xIQR

Where,

Q1 = First Quartile
Q3 = Third Quartile
IQR = Inter Quartile Range

## Bonferroni Correction

#### Formula:

α' = 1 - ( 1 - α ) 1/k

Where,

α' = Bonferroni Correction
α = Critical P Value
k = Number of Test

## Shannon Wiener Species Diversity Index

#### Formula:

H = -SUM[(pi) * ln(pi)]
E=H/Hmax

Where,

SUM = Summation
pi= Numbe of individuals of species i/total number of samples
S = Number of species or species richness
Hmax = Maximum diversity possible
E= Evenness=H/Hmax

## Signal to Noise Ratio

#### Formula:

SNR (or) S/N = μ/σ

Where,

μ - Mean,
σ - Standard Deviation,
SNR - Signal to Noise Ratio

## Reference Range Calculation using Normal Distribution

#### Formula:

Lower Limit = m - t0.975,n-1 x √((n+1)/n) x s.d
Upper Limit = m + t0.975,n-1 x √((n+1)/n) x s.d

Where,

t - Distribution.
s.d - Standard Deviation
n - Total Count
m - Mean

## Kuder-Richardson Formula 21

#### Formula:

Online statistics helps you in estimating the test reliability using Kuder-Richardson Formula 21 calculator. Where,

k - Number of questions
μ - Population mean score
σ2 - Variance of the total scores of all the people
ρKR21 - Reliability of the test

## Outlier Boundary

#### Formula:

Inter-quartile Range (IQR) = Q3 - Q1
Lower Outlier Boundary = Q1 - 1.5 x IQR
Upper Outlier Boundary = Q3 + 1.5 x IQR

Where,

Q1 = First Quartile
Q3 = Third Quartile

## Standard Deviation Index

#### Formula:

 SDI = Laboratory Mean - Consensus Group MeanConsensus Group SD

## Kanban

#### Formula:

Total Required Inventory (TRI) = Weekly Part Usage * Supplier Lead-time * Total locations for stock

Kanban = TRI / Container Capacity

## Estimate PERT Expected Time Duration

#### Formula

TE = (O + 4T + P) / 6

where,

TE = Pert Expected Time Duration,

O = Optimistic estimate,

T = Typical estimate,

P = Pessimistic estimate

## Black Scholes Model

#### Formula:

C = SN(d1)-Ke(-rt)N(d2)
where,

C = Theoretical call premium
S = Current stock price
t = time
K = option striking price
r = risk free interest rate
N = Cumulative standard normal distribution
e = exponential term (2.7183)
d1 = ( ln(S/K) + (r + (s2/2))t ) / s√t
d2 = d1 - s√t
s = Standard deviation of stock returns

## Relative Standard Deviation Calculator

#### Formula:

S = √ (Σ (x- x )2 / N - 1)
% RSD = S × 100/ x

Where,

Mean = X/N
X = Summation of x value
N = The count of mean values
S = Standard Deviation value
x = Mean of the data

## Root Locus of Open Loop Transfer Function

#### Formula:

G(s)H(s) = (s + 1) / (s3 + (4 * s2) + (6 * s) + 4)

Where,

G(s)H(s) = Root Locus of Open Loop Transfer Function
G(s) = Gain Function
H(s) = Feedback Function
s = S-Plane Value

## Relative Risk Reduction

#### Formula:

RRR = (EER - CER) /CER
EER = EE / ES
ES = EE + EN
CER = CE / CS
CS = CE + CN

Where,

RRR = Relative Risk Reduction
[ if (r is negative, then it is Relative Risk Reduction),
if (r is positive, then it is Relative Risk Increase) ]
EER = Experimental Event Rate
CER =Control Group Event Rate
EE = Experimental Events
EN = Experimental Non Events
ES = Experimental Total Subjects
CE = Control Group Events
CN = Control Group Non Events
CS = Control Group Total Subjects

## Possible Outcomes

#### Formula:

s = rn ( Case 1 )
s = n! / ( n - r! ) ( Case 2 )
s = ( n + r - 1 )! / ( r! * ( n - 1 )! ) ( Case 3 )
s = n! / (( n - r )! * r!) ( Case 4 )

Where,

s = Combination or Permutation
n = Total Number of Events
r = Number of value be Selected

Note:
Case 1 : Order is Important and Repetition is Allowed
Case 2 : Order is Important and Repetition is Notallowed
Case 3 : Order is Not Important and Repetition is Allowed
Case 4 : Order is Not Important and Repetition is Notallowed

#### Formula:

H4 = (0.55 * (h - l)) + c
H3 = (0.275 * (h - l)) + c
H2 = (0.183 * (h - l)) + c
H1 = (0.0916 * (h - l)) + c
L1 = c - (0.0916 * (h - l))
L2 = c - (0.183 * (h - l))
L3 = c - (0.275 * (h - l))
L4 = c - (0.55 * (h - l))

Where,

h = Previous Day High
l = Previous Day Low
c = Previous Day Close

## Williams Correction Factor

#### Formula:

q = 1+(a2 - 1)/(6 * n * v)

Where,

q = Williams Correction Factor
a = Number of Categories
n = Total Sample Size
v = Number of Degrees of Freedom

## Absolute Risk Reduction (ARR)

#### Formula:

Absolute Risk Reduction = Control Event Rate - Experimental Event Rate

Control Event Rate = c / (c + d)
Experimental Event Rate = a / (a + b)

Where,

a = Experimental Group Size
b = Control Group Size
c = Events in Experimental Group
d = Events in Control Group

## Raw Score

#### Formula:

Raw Score = μ + Z σ

Where,

μ = Mean
σ = Standard deviation
Z = Z score

## Upper Specification Limit

#### Formula:

Upper Specification Limit (USL) = ( c × 6 × s ) + LSL

Where,

c = Process Capability Index
s = Process Standard Deviation

## 91st Percentile

#### Formula:

R = 0.91x (N+1)

Where,

R = Percentile Rank
N = Number of Data

## Statistics Quartile

#### Formula:

(Q3-Q1)/(Q2-Q1)

Where,

Q1=First Quartile
Q3=Third Quartile
Q2=Second Quartile(Median)

## Control Limit | UCL

#### Formula:

Lower Limit Value = x - (l x s)
Upper Limit Value = x - (- l x s)

Where,

x = Control Mean
s = Control Standard Deviation
l = Control Limit you Wish to Evaluate

## 65th Percentile

#### Formula:

R = 0.65 x (N+1)

Where,

R = Percentile Rank
N = Number of Data

## Lower and Upper Fence

#### Formula:

Lower Fence = First Quartile - 1.5 x Interquartile Range
Upper Fence = Third Quartile + 1.5 x Interquartile Range

## Interdecile Range

#### Formula:

IDR = D90 - D10

Where,

IDR = Interdecile Range
D = Decile

## Annual Average Daily Traffic AADT

#### Formula:

Annual Average Daily Traffic = V / 365

Where,

V = Total Volume of Vehicle Traffic for a Year