Copyright © 2011 Pearson Education, Inc. Numbers in the Real World

Web and World Questions from 3C Web Questions: The 2010 Census (choose issue about accuracy or precision, did the bureau handle it well) Global Warming (find current estimates, how do scientists account for uncertainties in past data) World Questions: Random and Systematic Errors (news that gives measured quantity) Absolute and Relative (news report on some mistake in measure) Accuracy and Precision (news that you question A and P) Uncertainty in the News (find at least 2 numbers) Real world Rounding (3 diff. examples)

Copyright © 2011 Pearson Education, Inc. Slide 3-4 Unit 3D: The meaning and use of index numbers Index Numbers: The CPI and Beyond

3-D Copyright © 2011 Pearson Education, Inc. Slide 3-5 Index Numbers An index number provides a simple way to compare measurements made at different times or in different places. The value at one particular time (or place) must be chosen as the reference value.

3-D Finding an Index Number CN 1-3 During 2008, the average gasoline price reached a record high of $4.10 per gallon. Using the 1975 price as the reference value, find the following price index: 1. Gas at $4.10 per gallon 2. Gas at today’s price __________ per gallon 3. Gas at $2.50 per gallon Copyright © 2011 Pearson Education, Inc. Slide 3-6

3-D Copyright © 2011 Pearson Education, Inc. Slide 3-7 Example: Suppose the current price of gasoline is $3.20 per gallon. Using the 1975 price of 56.7¢ as the reference value, find the price index number for gasoline today. The current price is 564.4% of the 1975 price. Making Comparisons with Index Numbers

3-D Using the Gas Price Index CN Suppose it cost $7. to fill a gas tank in How much would it have cost to fill the same tank in 2005? 5. Suppose it cost $20. to fill a gas tank in How much would it have cost to fill the same tank in 1955? Copyright © 2011 Pearson Education, Inc. Slide 3-8

3-D Copyright © 2011 Pearson Education, Inc. Slide 3-9 Any reference value can be used to calculate an index number, but changing the reference value results in a different index number. Index Numbers: Changing the Reference Value Example:

3-D 1985 Index CN 6-8 Consider the 2008 record gas price of $ Using the 1985 price as the reference value, find its price index number. Compare to the index number where 1975 was the reference year. 7. Are both numbers valid? 8. What does each number tell us? Copyright © 2011 Pearson Education, Inc. Slide 3-10

3-D Copyright © 2011 Pearson Education, Inc. Slide 3-11 The Consumer Price Index The Consumer Price Index (CPI) is based on an average of prices for a sample of more than 60,000 goods, services, and housing costs. (overall rate of inflation) The CPI is computed and reported monthly by the US Bureau of Labor Statistics. The rate of inflation from one year to the next is usually defined as the relative change in the Consumer Price Index. *Inflation (prices and wages) goes up, deflation (prices and wages) goes down

3-D Copyright © 2011 Pearson Education, Inc. Slide 3-12 Consumer Price Index (table over a 33 year period) reference value is the average prices during period of

3-D CPI Changes CN (9-10) *Assume that the average price of your typical purchases has risen at the same rate as the CPI. 9. Suppose you needed $30,000 to maintain a particular standard of living in How much would you have needed in 2008 to maintain the same standard of living? 10. If someone needed $20,000 to maintain a certain standard of living in 1976, how much would be needed to maintain the same standard of living in 2008? Copyright © 2011 Pearson Education, Inc. Slide 3-13

3-D The Rate of Inflation * defined as the relative change in the CPI from one year to the next. Inflation rate from 1980 – 1982 was the relative increase in the CPI between those two years: = CPI (1981) – CPI (1980) 90.9 – 82.4 CPI (1980) 82.4 =.103 = 10.3% Copyright © 2011 Pearson Education, Inc. Slide 3-14

3-D Inflation Comparison CN (11-13) Find the inflation rate from 2007 to How does it compare to the inflation rate in the late 70’s? *hint look at inflation from What was the net inflation rate between ? 13. What was the net inflation rate between ? Copyright © 2011 Pearson Education, Inc. Slide 3-15

3-D Copyright © 2011 Pearson Education, Inc. Slide 3-16 Adjusting Prices for Inflation Given a price in dollars for year X ($ X ), the equivalent price in dollars for year Y ($ Y ) is where X and Y represent years.

3-D In other words…… CN (14) During the spring and summer of 2008, a sudden jump in gas prices became a huge issue. Pump prices peaked at $4.10 Ave. for the year $3.31 Some reporters noted that gas had sold for only $.65 in Was the 2008 price really more than 5 times as high? Copyright © 2011 Pearson Education, Inc. Slide 3-17

3-D Here’s the math… We can see how typical prices in 2008 compared to typical prices in 1978 by finding the ratio of the CPI’s. Approx Therefore the 1978 price of $.65 was equivalent to the 2008 price of $2.15. The 2008 average price of $3.31 was higher, but it was less than twice as high, not more than 5 times as high. Copyright © 2011 Pearson Education, Inc. Slide 3-18

3-D Baseball Salaries CN (15) In 1987 the mean salary for major league baseball players was $412,000. In 2008, it was $3,200,000. Compare the two salaries in “2008 dollars”. 15. How does the rise in baseball salaries compare to the overall rise in prices with inflation? Copyright © 2011 Pearson Education, Inc. Slide 3-19

3-D Computer Prices CN (16-17) According to computer performance tests, a Macintosh computer that cost $1000 in 2008 had computing power of greater than that of a supercomputer that sold for $30 million in If computer prices had risen with inflation, how much would the computing power of the 1985 supercomputer have cost in 2008? 17. What does this tell us about the cost of computers? Copyright © 2011 Pearson Education, Inc. Slide 3-20

3-D Other Index Numbers *index is often used for numbers that provide useful comparisons. CPI is only one of the many index numbers you’ll see in the news reports PPI: Producer Price Index which measures the prices that producers (manufacturers) pay for the goods they purchase. CCI: Consumer Confidence Index is based on a survey designed to measure consumer attitudes so that business can gauge whether people are likely to be spending or saving. BMI: Body Mass Index which provides a way of comparing people by height and weight, but it is designed without any reference values. Copyright © 2011 Pearson Education, Inc. Slide 3-21

3-D Practical Matters (CPI hot topic of debate) Your tax rate depends on the CPI SS and other programs are raised each year to keep up with CPI Spending an all gov. programs is determined by the CPI CPI influences how we perceive nearly all economic data (rise in wages) Does not measure true inflation, all things related to CPI could be wrong, many economists argue that CPI overstates the true rate of inflation. Standard calculation contains systematic errors. Tracks prices of items purchased by typical consumers. Does not factor standard of living improvement Slide 3-22