Statistics Cheatsheet — BitWithBite

Statistics

Statistics Complete Cheatsheet

Descriptive stats, probability, distributions, hypothesis testing, and regression — complete statistics reference.

📖 5 sections

⏰ 15 min read

✅ Quizzes included

🌙 Dark mode

01Descriptive Statistics▼

Mean

x-bar=sum(x)/n

Median

Middle value when sorted

Mode

Most frequent

IQR

Q3-Q1

Resistant to outliers.

Variance

s^2=sum(x-mean)^2/(n-1)

Sample variance.

Std dev

s=sqrt(variance)

68-95-99.7 rule for normal dist.

Symbol	Meaning
x-bar	Sample mean
mu	Population mean
s	Sample std dev
sigma	Population std dev
n	Sample size

02Probability▼

P(A)

0 to 1 range. P(certain)=1, P(impossible)=0

Complement

P(A')=1-P(A)

Addition

P(AuB)=P(A)+P(B)-P(AnB)

Multiplication

P(AnB)=P(A|B)*P(B)

Independent

P(AnB)=P(A)*P(B)

Conditional

P(A|B)=P(AnB)/P(B)

STATSProbability examples

# Deck of 52 cards
P(Ace)=4/52=1/13
P(Red or Ace)=26/52+4/52-2/52=28/52

# Independent
P(Head AND Head)=0.5*0.5=0.25

# Conditional
P(2nd Ace | 1st was Ace)=3/51

03Distributions▼

Distribution	Mean	Variance	Use when
Binomial(n,p)	np	np(1-p)	Fixed n trials, constant p
Poisson(lambda)	lambda	lambda	Rare events, fixed time
Normal(mu,sigma^2)	mu	sigma^2	Continuous, bell-shaped
Uniform(a,b)	(a+b)/2	(b-a)^2/12	All outcomes equally likely

STATSBinomial

P(X=k)=C(n,k)*p^k*(1-p)^(n-k)

Example: 10 flips, p=0.5, P(X=6)
=C(10,6)*0.5^6*0.5^4
=210*0.015625*0.0625=0.205

04Hypothesis Testing▼

Null hypothesis: no effect. We try to disprove it.

Alternative hypothesis: our claim.

p-value

Prob of result if H0 true. p

alpha

Significance level, usually 0.05.

Type I error

Reject H0 when true (false positive). Rate=alpha.

Type II error

Fail to reject H0 when false (false negative). Rate=beta.

STATSTest steps

1. State H0 and H1
2. Set alpha (0.05)
3. Choose test statistic
4. Calculate: t=(x-bar - mu0)/(s/sqrt(n))
5. Find p-value
6. p

❓ Quiz

p<0.05 in hypothesis testing means?

p-value < alpha means the result is statistically significant — reject null hypothesis H0.

05Regression▼

Pearson r

-1 to 1

|r|>0.7 strong, <0.3 weak.

R-squared

0 to 1

Variance explained by model.

Regression line

y-hat=a+bx

b=slope, a=intercept.

Slope

b=r*(sy/sx)

Intercept

a=y-bar - b*x-bar

Point (x-bar,y-bar) on line.

⚠️

Correlation does NOT imply causation! Even r=1 does not prove one variable causes the other.