Section 5.2: BUY OR SELL A CAR OBJECTIVES
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1 Section 5.2: BUY OR SELL A CAR OBJECTIVES Compute mean, median, mode, range, quartiles, and interquartile range. Key Terms statistics data measures of central tendency mean arithmetic average outlier median ascending order descending order skew resistant range quartiles lower quartile upper quartile subscripts interquartile range (IQR) mode bimodal Chapter 5: Automobile Ownership 1
2 How can statistics help you negotiate the sale or purchase of a car? Brainstorm some ideas! In this section, we will examine: Measures of Central Tendency are single numbers designed to represent a typical value for the data. Mean, Median, Mode Measures of Central Tendency 1. Mean: the arithmetic average; the sum of a set of data divided by the number of elements in the set. 2. Median: the middle value or the mean of the two middle values, when the data is arranged in numerical order. 3. Mode: the value that appears most often. It is possible to have more than one mode or no mode. If there are two modes, the data set is bimodal. 4. Outlier: a piece of data that is extremely different than the rest of the data. Note: When there are outliers, the mean is often not a good representation of the data and the median is often the better data value to use. 5. When the mean of a data set is not equal to the median, the data is skewed. Chapter 5: Automobile Ownership 2
3 Example 1 Joey 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 Joey to consider for his SUV? Example 2 Mr. Gellar is looking for a classic 1967 Firebird. He finds these prices online: $18,000, $77,000, $22,000, $21,200, $19,000, $17,500, and $22,500. He computes the mean as $28, This number doesn t seem to be a good representative of the data. How can he find a better representation? Chapter 5: Automobile Ownership 3
4 Using the Calculator Find the mean, median and mode of the following data: 15, 22, 32, 31, 52, 41, 11 Step 1: Enter the data into the calculator. Press the STAT button and choose EDIT. Type in data. Press ENTER after each entry. Step 2: Perform 1 Variable Statistical Calculations Press STAT and choose CALC Select 1 VAR STATS You are now back on the home screen. Tell the calculator what list to use by pressing 2 ND 1 for L1. Press ENTER and CALCULATE. Arrow down to view the next screen Chapter 5: Automobile Ownership 4
5 Arrow down to view this information: Q1: median of lower half of data; 25 th percentile, ¼ of data lies below Med=Q2: 50 th percentile, ½ of data lies below and ½ data lies above Q3: median of upper half of data; 75 th percentile, ¾ of data lies below maxx=q4: represents 100% of the data Example 3 Find the mean, median and mode 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? Chapter 5: Automobile Ownership 5
6 More Vocabulary 6. Range: a measure that shows dispersion, how spread out the data are, and is the difference between the greatest and least numbers in the data. 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. More Vocabulary 7. Quartiles: three values represented by Q,Q,Q and divide the distribution of data into four subsets that each contain 25% of the data. (a) Lower Quartile, or the first quartile, is represented by Q and 25% of the numbers in the data set are at or below Q. (b) Median, or the second quartile, is represented by Q and half the numbers in the data set are below Q and half are below Q. (c) Upper Quartile, or the third quartile, is represented by Q and 75% of the numbers in the data set are at or below Q. (d) Maximum value in the data set is represented by Q because 100% of the numbers are at or below that number. Chapter 5: Automobile Ownership 6
7 Example 5 Find the quartiles for the tire pressures of cars at an auto clinic. 15, 17, 21, 25, 31, 32, 32, 32, 34 What is the difference between Q and Q? More Vocabulary 8. Interquartile Range: the difference, Q Q. The IQR gives the range of the middle 50% of the numbers in the data set. A small interquartile range indicates that the middle 50% of the data is clustered together. A large interquartile range indicates that the middle 50% of the data is more spread out. Chapter 5: Automobile Ownership 7
8 More Vocabulary 9. Calculating outliers: the IQR is used to calculate and identify outliers. Outliers may occur on the lower or upper end of the data set. Calculate the boundary value for lower outliers: Q 1.5 IQR Calculate the boundary value for upper outliers: Q 1.5 IQR If a data value lies outside a boundary value, then the data value is characterized as an outlier of the data set. This outlier lies below the lower limit. This outlier lies above the upper limit. The lower limit is the boundary value for lower outliers. The upper limit is the boundary value for upper outliers. Chapter 5: Automobile Ownership 8
9 Example 7 Find the outliers for these tire prices: $45, $88, $109, $129, $146, $189, $202, $218, and $545 Chapter 5: Automobile Ownership 9
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