Formula Sheet Chapters 1 to 10 PDF

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Summary

Formula sheet (Chapters 1 - 10 )Quantitative Data Description:Q3: 75thpercentileQ1: 25thpercentileRange=Max-Min𝐼𝑄𝑅 = 𝑄3 − 𝑄Outlier Rule: 𝑦 < 𝑄1 − 1 ∗ 𝐼𝑄𝑅 or 𝑦 > 𝑄3 + 1 ∗ 𝐼𝑄𝑅𝑦̅ =∑𝑦𝑛Standard Deviation = √Variance𝑠 =√∑(𝑦 − 𝑦̅)2𝑛 − 1𝑧 =𝑦 − 𝜇𝜎"population"𝑧 =𝑦 − 𝑦̅𝑠"sample"𝐶𝑉 =𝑠𝑦̅Association, correl...

Description

Formula sheet (Chapters 1 - 10) Quantitative Data Description: Q3: 75th percentile Q1: 25th percentile Range=Max-Min 𝐼𝑄𝑅 = 𝑄3 − 𝑄1

Outlier Rule: 𝑦 < 𝑄1 − 1.5 ∗ 𝐼𝑄𝑅 or 𝑦 > 𝑄3 + 1.5 ∗ 𝐼𝑄𝑅 𝑦 =

∑𝑦 𝑛

Standard Deviation = √Variance 𝑠=√

∑(𝑦 − 𝑦)2 𝑛−1

𝑦−𝜇 "population" 𝜎 𝑦 − 𝑦 𝑧= "sample" 𝑠 𝑠 𝐶𝑉 = 𝑦 𝑧=

Association, correlation and regression: 𝑟=

𝑟=

∑ 𝑧𝑥 𝑧𝑦

𝑛−1 ∑(𝑥 − 𝑥 )(𝑦 − 𝑦)

√∑(𝑥 − 𝑥 )2 ∑(𝑦 − 𝑦)2

=

𝑦 = 𝑏0 + 𝑏1 𝑥 where 𝑏1 = 𝑟 𝑒 = 𝑦 − 𝑦 𝑠𝑒 = √

∑ 𝑒2

𝑛−2

𝑍󰆹𝑦 = 𝑟𝑍𝑥

∑(𝑥 − 𝑥 )(𝑦 − 𝑦)

𝑠𝑦

𝑠𝑥

(𝑛 − 1)𝑠𝑥 𝑠𝑦

and 𝑏0 = 𝑦 − 𝑏1 𝑥

Formula sheet (Chapters 1 - 10)

Probability: 𝑃(𝐴) =

No. of outcomes in A Total no. of outcomes

𝑃(𝐴) = 1 − P(𝐴𝐶 )

𝑃(𝐴 or 𝐵 ) = 𝑃 (𝐴 ∪ 𝐵 )

𝑃(𝐴 and 𝐵 ) = 𝑃(𝐴 ∩ 𝐵 )

𝑃(𝐴 or 𝐵 ) = 𝑃 (𝐴) + 𝑃(𝐵 ) − 𝑃(𝐴 and 𝐵) 𝑃(𝐴|𝐵 ) =

𝑃(𝐴 and 𝐵) 𝑃(𝐵)

𝑃(𝐴 and 𝐵 ) = 𝑃(𝐴|𝐵 )𝑃 (𝐵 ) = 𝑃(𝐵 |𝐴)𝑃(𝐴) Discrete Random Variables: 𝐸 (𝑋) = 𝜇 = ∑ 𝑥𝑃(𝑥 )

𝑉𝑎𝑟(𝑋) = 𝜎 2 = ∑(𝑥 − 𝜇 )2 𝑃(𝑥) 𝑆𝐷(𝑋) = √𝑉𝑎𝑟(𝑋)

𝑛 Binomial: 𝑃 (𝑋 = 𝑥) = 𝑛 C𝑥 𝑝 𝑥 𝑞𝑛−𝑥 = ( ) 𝑝 𝑥 𝑞𝑛−𝑥 = 𝑥 If X is Binomial then E(X)= 𝑛𝑝

Continuous Random Variables

𝑆𝐷(𝑋) = √𝑛𝑝𝑞

1

Uniform Distribution: 𝑓(𝑥 ) = {𝑏−𝑎 0,

,

(𝑏 − 𝑎)2 𝑎+𝑏 , 𝑉𝑎𝑟(𝑋) = 𝐸 (𝑋) = 2 12

if 𝑎 ≤ 𝑥 ≤ 𝑏

otherwise

𝑛! 𝑝 𝑥 (1 𝑥!(𝑛−𝑥)!

− 𝑝)𝑛−𝑥

𝑃(𝑐 ≤ 𝑋 ≤ 𝑑) = 𝑏−𝑎

𝑑−𝑐

Adding two normally distributed random variables:

𝑋~𝑁(𝜇𝑥 , 𝜎𝑥 ) and 𝑌~𝑁(𝜇𝑦 , 𝜎𝑦 ) and 𝐿 = 𝑋 + 𝑌 then 𝐿~𝑁(𝜇𝑥 + 𝜇𝑦 , √𝜎𝑥2 + 𝜎𝑦 2 )

𝑋~𝑁(𝜇𝑥 , 𝜎𝑥 ) and 𝑌~𝑁(𝜇𝑦 , 𝜎𝑦 ) and 𝐾 = 𝑋 − 𝑌 then 𝐾~𝑁(𝜇𝑥 − 𝜇𝑦 , √𝜎𝑥2 + 𝜎𝑦 2 )

Formula sheet (Chapters 1 - 10) Sampling Distributions:

𝑥

If conditions are satisfied, the sampling distribution of a proportion, 𝑝 = , is Normally distributed with 𝜇 (𝑝 ) = 𝑝 and 𝑆𝐷 (𝑝 ) = √

𝑝(1−𝑝) 𝑛

Success/Failure condition: 𝑛𝑝 ≥ 10 and 𝑛(1 − 𝑝) ≥ 10

𝑛

If conditions are satisfied, the sampling distribution of a mean, 𝑦, is Normally 𝜎 distributed with 𝜇 (𝑦) = 𝜇 and 𝑆𝐷 (𝑦) = 𝑛

Large sample condition: 𝑛 ≥ 30. 𝑆𝐸 (𝑝 ) = √

𝑆𝐸 (𝑦) =

𝑝(1−𝑝) 𝑛

𝑠 √𝑛

√

if 𝑆𝐷(𝑝 ) not available.

if 𝑆𝐷(𝑦) not available....