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Research School of Finance, Actuarial Studies and Applied Statistics STAT7055 Tutorial Week 2 NingNing Wang (Tony) Research School of Finance, Actuarial Studies and Applied Statistics Updated 28th Feb 2017

Introduction Miscellaneous about the course Tutorial 1

Introduction NingNing Wang (Tony) Bachelor and Master of Actuarial Studies in ANU u4975898@anu.edu.au www.linkedin.com/in/ningningwang/ Consultation time Wed 1pm~4pm CBE 3.09 (Statistics Consultation Room)

Your assessments: Quiz 5% (or 0%) Mid 30% (or 35%) Final 65%

Communication – in English Send any questions or any concerns to my email address using your ANU email Attend the consultations if you have any questions Do your homework Finish the tutorial questions At least read through them

Topic 1 - Descriptive Statistics Tutorial Week 2 Topic 1 - Descriptive Statistics

Summary Population vs sample Parameters (μ, σ) vs statistics 𝑋 , s Categorical vs Numerical Nominal vs Ordinal Discrete vs Continuous

Central Tendency: mean (arithmetic), median, mode Quantile & Percentile Range & IQR Variance and Covariance Correlation Coefficient

Question 1 Variable Features Estimated Price Number of Bedrooms Size Pool Present Distance from Civic Insulation rating Suburb Number of bathrooms Type of Internet

Question 1 Variable Features Estimated Price Continuous Number of Bedrooms Discrete (Count) Size Pool Present Nominal (Yes/No) Distance from Civic Insulation rating Ordinal (categories) Suburb Nominal Number of bathrooms Discrete Type of Internet

Question 2 Let X be the marketing expenditure Y be the number of sales Z be the number of rainy days

Question 2 Month Xi Yi ( 𝑿 𝒊 − 𝑿 )( 𝒀 𝒊 − 𝒀 ) 1 4150 778 1944971.88 2 ( 𝑿 𝒊 − 𝑿 )( 𝒀 𝒊 − 𝒀 ) 1 4150 778 1944971.88 2 3000 779 3103828.13 3 2500 4200 -8621559.38 4 10600 250 -6961146.88 5 12000 300 -8818621.88 6 8000 6000 8107378.13 7 1500 1319315.63 8 6850 500 -998490.63 Mean = 6075 Mean = 1788.375 ∑=-10924325.00

Question 2 𝑠 𝑋 =𝑐 𝑣 𝑋 ∗ 𝑋 =3905.3077, 𝑠 𝑌 =𝑐 𝑣 𝑌 ∗ 𝑌 = 2135.3603 𝑠 𝑋 =𝑐 𝑣 𝑋 ∗ 𝑋 =3905.3077, 𝑠 𝑌 =𝑐 𝑣 𝑌 ∗ 𝑌 = 2135.3603 𝑠 𝑋𝑌 = −10924325 8−1 =−1560617.86 𝑟 𝑋𝑌 = −1560617.86 3905.3077∗2135.3603 =−0.1871 𝑍 =12.125, 𝑠 𝑧 =𝑐 𝑣 𝑧 ∗ 𝑍 =7.9541 𝑟 𝑍𝑌 = 14012.23 7.9541∗2135.3603 =0.8250

Question 5 Data n=11 13 26 22 16 18 28 14 15 15 17 25 𝜇=19, 𝜎 2 = 1 𝑁 𝑖=1 𝑁 𝑋 𝑖 −𝜇 2 = 282 11 =25.6364

Question 5 Sample 𝑿 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 13,22,18,16 17.25 1233 26,15,17,15 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 13,22,18,16 17.25 1233 26,15,17,15 18.25 1415 14,18,15,25 18 1370 25,14,16,17 1366 13,26,25,18 20.5 1794

Question 5 Sample 𝑿 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 − 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 𝒏 𝒔 𝟐 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 − 𝒊=𝟏 𝒏 𝑿 𝒊 𝟐 𝒏 𝒔 𝟐 (using n-1) 𝒔 ∗𝟐 (using n) 13,22,18,16 17.25 1233 42.75 14.25 10.6875 26,15,17,15 18.25 1415 82.75 27.5833 20.6875 14,18,15,25 18 1370 74 24.6667 18.5 25,14,16,17 1366 70 23.3333 17.5 13,26,25,18 20.5 1794 113 37.6667 28.25 average 25.5 19.125

Question 3 Mean = 18.55 9 11 12 12 12 13 14 20 20 35 46 Median = 13, Mode = 12 𝐿 𝑝 = 𝑛+1 𝑝 100 L25 = 3, L75 = 9, L10 = 1.2, L60 = 7.2 9+0.2*(11-9)=9.4, 14+0.2*(20-14)=15.2 L=7.25, 60.4167