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5.2 Buy or Sell a Car. Ch 5: Automobile Ownership. Answer the following questions on a piece of paper. What is more important to you, the mechanical condition of the car or its appearance? Why? Do you think the appearance is a reflection of the mechanical condition of the car?
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5.2 Buy or Sell a Car Ch 5: Automobile Ownership
Answer the following questions on a piece of paper • What is more important to you, the mechanical condition of the car or its appearance? • Why? • Do you think the appearance is a reflection of the mechanical condition of the car? • How do you think statistics can help you negotiate the buying or selling of a car
Research is key to buying and selling a car • Kelly blue book (www.kbb.com) • Edmunds (www.edmunds.com) • When researching you want to compile a list of prices of the car you want • The numbers that you compile are called data • We can use measures of central tendency (single numerical values that represent a “typical” value of the data) to help analyze that data
First measure of central tendency • The mean, or arithmetic average is the first measure of central tendency we will talk about • Add data together and divide by how many values are apart of the data set
Example 1 • Jason wants to sell his Ford SUV. He compiles these prices from the Internet for cars similar to his: $11,000, $9,900, $12,100, $10,500, and $9,000. What is a reasonable price for Jason to consider for his SUV?
Example 2 • Dory is looking for a classic 1967 Firebird. She finds these prices on the Internet: $18,000, $77,000, $22,000, $21,200, $19,000, $17,500, and $22,500. She computes the mean as $28,171.43. This number doesn’t seem to be a good representative of the data. How can she find a better representation?
Different aspects of a data set • Some data may contain outliers, data values that are extremely different than the rest of the data • When there are outliers, the median is often the best measure of central tendency • The median is the middle number when the data set is placed in ascending (least to greatest) or descending order (greatest to least)
Different aspects of a data set • When the median and the mean are not equal to each other, we say the data set is skewed • The median is resistant to extreme numbers whereas the mean is not
Check your understanding • Find the mean and median of the following prices for a used car extended warranty: $1,200, $1,650, $1,500, $2,000, $1,400, $1,850, and $1,600. Is the data skewed?
Example 3 • Find the median of the following used car prices: $6,700, $5,800, $9,100, $8,650, $7,700, and $7,800.
Example 4 • Prices found online for the same GPS navigation system are $295, $345, $199, $225, and $200. Find the range of the GPS prices.
Range • The range of a data set is how spread out the data set is. • Subtract the least number from the greatest number in the set and you have the range
Group Activity • Go on Kelly Blue Book and choose a car • Find out what the price should be for a certified used car of your choice • Now go on Edmunds.com and find a list of prices for that car. • Write down 10 prices for a certified used car • Find the mean, median, mode and range • Is the data skewed? • How close to KBB is your data set?
Finding out more about how the data is dispersed… • Data can be divided into 4 subsets using quartiles, Q1, Q2, and Q3 • Q1, also known as the lower quartile. 25% of the data is at or below Q1 • Q2 is equal to the median and 50% of the data are at or below Q2 • Q3is called the upper quartile and 75% of the data is at or below Q3 • Q4 is the maximum number in the set
Example 5 Find the quartiles for the tire pressures of cars at an auto clinic. 15, 17, 21, 25, 31, 32, 32, 32, 34 Tire pressure is measured in psi—pounds per square inch.
Example 6 • What is the difference between Q1 and Q3 from the data set in Example 5? • The difference meaning subtracting Q1 from Q3, this is called the interquartile range (IQR)
Example 7 • Find the outliers for these tire prices: $45, $88, $109, $129, $146, $189, $202, $218, and $545 • The IQR is used to find outliers
Example 8 • Each year, the 880 seniors in North Shore High School vote for one of the 110 teachers to receive the annual yearbook dedication. The teacher who receives the most votes wins. Can a teacher who receives 9 votes win, if every senior votes? • The mode is the most occurring item, in this case teacher votes • There can be no mode, or multiple modes • Data with 2 modes is called bimodal
Ch 5 Asnmt 2 • Pg. 229 #5 – 11, 14, 15