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2. 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

3. Introduction
Miscellaneous about the course
Tutorial 1

4. Introduction NingNing Wang (Tony)
Bachelor and Master of Actuarial Studies in ANU
Consultation time
Wed 1pm~4pm CBE 3.09 (Statistics Consultation Room)

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

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

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

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

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

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

11. 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

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

13. 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 2
3000
779 3
2500
4200 4
10600
250 5
12000
300 6
8000
6000 7
1500 8
6850
500
Mean = 6075
Mean = ∑=

14. Question 2 𝑠 𝑋 =𝑐 𝑣 𝑋 ∗ 𝑋 =3905.3077, 𝑠 𝑌 =𝑐 𝑣 𝑌 ∗ 𝑌 = 2135.3603
𝑠 𝑋 =𝑐 𝑣 𝑋 ∗ 𝑋 = , 𝑠 𝑌 =𝑐 𝑣 𝑌 ∗ 𝑌 =
𝑠 𝑋𝑌 = − −1 =−
𝑟 𝑋𝑌 = − ∗ =−0.1871
𝑍 =12.125, 𝑠 𝑧 =𝑐 𝑣 𝑧 ∗ 𝑍 =7.9541
𝑟 𝑍𝑌 = ∗ =0.8250

15. Question 5
Data n=11
𝜇=19, 𝜎 2 = 1 𝑁 𝑖=1 𝑁 𝑋 𝑖 −𝜇 2 = =

16. 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

17. 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
26,15,17,15
18.25
1415
82.75
14,18,15,25 18
1370 74
18.5
25,14,16,17
1366 70
17.5
13,26,25,18
20.5
1794
113
28.25
average
25.5
19.125

18. Question 3
Mean = 18.55
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, *(20-14)=15.2
L=7.25,