Chapter 1: Intro

Graphs for Categorical: Pie / Bar Graphs for Quantitative(Discrete / Continuous) :

Dot Plot / Stem & Leaf / Histogram / Timeplot Describe: Centre/Mode, Spread, Shape, Outlier Perfect bell-shaped: Mean = Median = Mode Skewed Data: Mode > Median > Mean

Chapter 2: Representation of Data

- Midrange = Lowest+Highest

2- Range = Highest value – Lowest value

- Mid-quartile = Q1+Q 32

Chapter 3: Descriptive Analysis

- 1.5IQR below Q1 OR 1.5IQR above Q3: Outliers- Relation ≠ Causation, as one ↑, the other ↑- Response Variable (Dependent Variable, y) VS

Explanatory Variable (Independent Variable, x)- Population Variance VS Sample Variance:

δ2 ∑ (x i−¿ µ)2

N¿= VS s2 =

∑ (x i−¿ x )2

n−1¿

- Chebyshev’s Inequality:

At least (1 - 1

K2¿∗100%, k = s.d.

Chapter 4: Gathering Data

Sample Survey: Simple Random, Cluster, Stratified, Systematic

Experiment: Control, Random, Blinding, Large

Observational Studies: Sample Survey, Retrospective, Prospective

Avoid Convenience SamplingStatistical Significance ≠ Practical Significance

Chapter 5: ProbabilityProbability is the relative frequency with which the event occurs

- SR VS LR, Cumulative Freq fluctuates in Short Run- P(A) = 1 – P(A)- P(A OR B) = P(A) + P(B) – P(A ∩ B),where P(A ∩ B) = 0 if disjoint- P(A ∩ B) = P(A) x P(B|A) = P(B) x P(A|B)- If independent, P(A ∩ B) = P(A) x P(B)

Chapter 6: Probability Distribution (Experiment)

Discrete

µ = E(X) δ = √∑ ¿¿¿

= ∑ (x . P ( x )) = √∑ (¿x2 .P ( x )−µ2)¿

Binomialµ = np δ = √npq- Each trial has only 2 outcomes- Each trial has same probability, p- Trials are independent of each other- No. of successes, X is an integer from [0, n]Binomial close to bell-shape if np & nq ≥ 15- P(x) = nCx.Px.(1-P)n-x

Chapter 7: Sampling Distributions (Sample)

Mean = p ; standard error = √ p (1−p)n

Central Limit Theorem applies when n ≥ 30

X ~ N(µ, δ2) Z ~ N(0, 1) ProbabilityWhen µ and δ are given:

Find: P(X) P(X )

Use: Z = x−µδ

Z = x−µδ /√n

Chapter 8: Statistical Inference(One Population)

- Point Estimate: Single value of best guess- Interval Estimate: Interval of numbers which

parameter believed to fall inInterval = point estimate ± margin of error

- Sample size ↑, SE ↓ despite high CI- CI for Proportions:

p = p̂ ±Z a2

.√ pqn- CI for Means (with δ VS w/o δ)

µ = x± Z a2

.δ

√n VS µ = x± t a2

.S

√n , df = n–1

- Pooled p, p̂

p̂=x1+ x2n1+n2

- Derive Sample Size:

n= p̂ q̂(Z a2

E)

2

, p̂∧ q̂ are parameters

Chapter 9: Hypothesis Step 1:H₀: µ = µ₀ VS Hₐ: µ ≠ µ₀

Step 2:Variable is quantitative/categorical

Incorrect Error P Correct Type PReject true H₀ Type I α True H₀ A 1-α

Fail to reject H₀ Type II β False H₀ B 1-β

Data obtained randomized?Population distribution approximately normal (SIZE)?

Step 3 / 4:Compute test statisticDerive p-value

Step 5: Small p, reject H₀ and conclude that…Large p, evidence to support H₀