Stats1_Pattern_Bank

Stats 1: Pattern Bank & Mental Algorithms

IMPORTANT

Master List: Every standard question type in Stats 1.

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Week 1: Data Collection

Pattern 1.1: Sample vs Population

Question: “Surveyed 4 IITs to infer about all Engineering Colleges.” Algorithm:

1. Target: Who do we want to know about? (All Colleges $\to$ Population).
2. Source: Who gave data? (4 IITs $\to$ Sample).

Pattern 1.2: Scales (NOIR)

Question: “Scale of ‘Temperature in Celsius’?” Algorithm:

1. Order?: Yes.
2. Zero?: Is $0^{\circ }$ ‘no heat’? No. $\to$ Interval.

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Week 2: Visualization

Pattern 2.1: Pie Chart Aggregate

Question: “Total 500. A(20%), B(30%). Find Total(A+B).” Algorithm:

1. Sum %: $20+30=50\%$.
2. Calc: $0.5\times 500=250$.

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Week 3: Central Tendency

Pattern 3.1: Missing Frequency

Question: “Mean is 5. Data: 2, 8. Freq: $x,3x$.” Algorithm:

1. Sum $f$: $4x$.
2. Sum $fx$: $2(x)+8(3x)=2x+24x=26x$.
3. Eq: $26x/4x=6.5$. (If mean was given as 6.5).
   • Note: Usually $x$ cancels out or you solve for it.

Pattern 3.2: Combined Mean

Question: “Class A (Mean 10, $n=20$), Class B (Mean 20, $n=30$). Combined Mean?” Algorithm:

1. Total Sum: $(10\times 20)+(20\times 30)=200+600=800$.
2. Total $n$: $20+30=50$.
3. Mean: $800/50=16$.

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Week 4: Dispersion

Pattern 4.1: Outlier Check

Question: “Data: 1, 5, 9. Is 20 an outlier?” Algorithm:

1. IQR: Find $Q1,Q3$. $IQR=Q3-Q1$.
2. Fence: $Q3+1.5(IQR)$.
3. Check: Is $20>\text{Fence}$? Yes $\to$ Outlier.

Pattern 4.2: Variance Transformation

Question: “Var(X) = 10. $Y=-2X+5$. Var(Y)?” Algorithm:

1. Scale: $(-2{)}^2=4$.
2. Shift: Ignore $+5$.
3. Calc: $10\times 4=40$.

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Week 5-6: Counting

Pattern 5.1: “Together” Bundle

Question: “Arrange 3 Boys, 2 Girls. Girls sit together.” Algorithm:

1. Bundle Girls: $\{G_1,G_2\}=1$ Unit.
2. Outer: 3 Boys + 1 Unit = 4 Entities $\to 4!$.
3. Inner: 2 Girls $\to 2!$.
4. Total: $4!\times 2!$.

Pattern 6.1: Handshakes

Question: ”$n$ people. Total handshakes?” Algorithm:

1. Combo: ${}^n{C}_2$.

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Week 7-8: Probability

Pattern 7.1: At Least One

Question: “Prob of hitting target at least once in 3 tries (p=0.2)?” Algorithm:

1. Fail Prob: $1-0.2=0.8$.
2. Fail All: $0.8^3=0.512$.
3. Result: $1-0.512=0.488$.

Pattern 8.1: Bayes (Disease Test)

Question: “Pos Test. Prob of Disease?” Algorithm:

1. True Pos: $P(D)\times P(Pos|D)$.
2. False Pos: $P(NoD)\times P(Pos|NoD)$.
3. Result: $\frac{\text{True Pos}}{\text{True Pos}+\text{False Pos}}$.