Car SAC

.docx

School

St Joseph's College *

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Course

Subject

Economics

Date

May 13, 2024

Type

docx

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Uploaded by MateInternetWolverine46 on coursehero.com

Buying a Car New cars are safer to drive, but they are expensive to buy. This SAC explores the prices of cars of various ages and various makes and attempts to find a satisfactory relationship between the age of a car and its price. SESSION ONE Andrew is an 18 year old who would like to buy a recent model car because of the additional safety features. He goes onto carsguide.com.au and collates the following information about the prices of 2009 model cars that are bought now. All vehicles are standard automatic petrol sedans and the prices are the averages for a private sale for that model. 2009 Car model Price $(AUS) 2009 Car model Price $(AUS) BMW 3 35i $73400 Kia Cerato $11800 Dodge Avenger $16000 Kia Rio $10100 Ford Falcon $15500 Mazda 3 $16700 Ford Focus $14400 Mercedes Benz E200K $58400 Ford Mondeo $17400 Mercedes Benz E280 $64300 Holden Barina $11600 Mercedes Benz E500 $97500 Holden Berlina $22100 Nissan Tiida $12200 Holden Caprice $38100 Subara Liberty $20300 Holden Commodore $16830 Toyota Camry Altise $15400 Holden Statesman $37800 Toyota Corolla $14900 Honda Accord V6 $23500 Toyota Yaris $11800 Honda Civic $17300 Volvo S40 $28000 Hyundai Accent $11700 Volvo S60 $28100 Hyundai Elantra $15400 Volvo S80 $44400 Hyundai Sonata $16600 Page 1

(1A) Complete the following frequency table for the 2009 car price data. (2 marks) Price Range Frequenc y $0<-$10000 $10000<- $20000 $20000<- $30000 $30000<- $40000 $40000<- $50000 $50000<- $60000 $60000<- $70000 $70000<- $80000 $80000<- $90000 $90000<- $100000 (1B) Construct a histogram of the 2009 car price data on the grid below. (3 marks) Page 2

(1C) Describe the 2009 Car price data in terms of shape, centre and spread. (3 marks) (1D) There are a number of outliers in the 2009 Car price data. Show which values are outliers demonstrating the calculation that you used to determine that they are outliers. (3 marks) Page 3

SESSION TWO Andrew is wondering about whether some vehicles hold their value better than others. He explores the current prices of a number of vehicles that were produced in both 2005 and 2009 and collates the following information including the mean and standard deviation of the prices for each year: 2009 Car Price ($) 2005 Car Price ($) Ford Falcon 15,500 7,700 Ford Focus 14,400 7,300 Holden Berlina 22,100 9,700 Holden Caprice 38,100 15,400 Holden Commodore 16,830 7,300 Holden Statesman 37,800 12,800 Honda Accord V6 23,500 11,600 Honda Civic 17,300 9,600 Hyundai Elantra 15,400 7,500 Hyundai Sonata 16,600 6,600 Kia Cerato 11,800 7,700 Kia Rio 10,100 6,000 Mazda 3 16,700 11,500 Subara Liberty 20,300 12,400 Toyota Camry Altise 15,400 7,250 Toyota Corolla 14,900 9,000 Volvo S40 28,000 14,800 Volvo S60 28,100 14,800 Average 20157.22 9941.67 Standard deviation 8099.91 3080.98 (2A) Randomly select one of the cars from this data, stating below the method that you used to select this vehicle. (2 marks) Page 4

(1B) Calculate the standardised score for your selected vehicle for the 2009 data correct to 2 decimal places. (2 marks) (1C) Comment on the meaning of this standardised score for your selected vehicle. (2 marks) (1D) Calculate the standardised score for the same vehicle for the 2005 car data correct to 2 decimal places. (2 marks) (1E) Comment on the meaning of any difference in the standardised score for your selected vehicle. (2 marks) Page 5

(1F) Andrew decides that he would like to buy a vehicle that has a standard score of 1 for each of 2009 and 2005. Using the given averages and standard deviations, calculate the amount this vehicle would have decreased in price on average each year between 2005 and 2009. (4 marks) (1G) Calculate the five figure summary for the prices of cars from each of the years 2009 and 2005 and hence complete the table below. (2 marks) Min Q1 Med Q3 Max 2009 vehicles 2005 vehicles (1H) Construct parallel boxplots for the price data from 2005 and 2009 on the grid below. (4 marks) Page 6

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