1.  Statistical Reasoning Chapter 2- Measurement in Statistics

2. Data Types  Qualitative – Quantitative – p. 54  Continuous – Discrete – p. 55  Levels: nominal, ordinal, interval, ratio – p. 56

3. Errors  Random & Systematic – p. 59  Absolute & Relative Exercise: Choose 1 team member - measure height – calculate absolute & relative differences from the nearest inch to the nearest CM.

4. Identify the variable as either quantitative or qualitative: A person’s social security number a.Quantitative b.Qualitative

5. Identify the variable as either quantitative or qualitative: A person’s social security number a.Quantitative b.Qualitative

6. Identify the variable as either quantitative or qualitative: The number of textbooks owned by a student a.Quantitative b.Qualitative

7. Identify the variable as either quantitative or qualitative: The number of textbooks owned by a student a.Quantitative b.Qualitative

8. Identify the number as either continuous or discrete: The number of 1916 dimes still in circulation a.Continuous b.Discrete

9. Identify the number as either continuous or discrete: The number of 1916 dimes still in circulation a.Continuous b.Discrete

10. Identify the number as either continuous or discrete: The voltage of electricity in a power line a.Continuous b.Discrete

11. Identify the number as either continuous or discrete: The voltage of electricity in a power line a.Continuous b.Discrete

12. Determine which of the four levels of measurement is most appropriate. A taste tester rates five brands of salsa from A (best) to E (worst). a.Nominal b.Ordinal c.Interval d.Ratio

13. a.Nominal b.Ordinal c.Interval d.Ratio Determine which of the four levels of measurement is most appropriate. A taste tester rates five brands of salsa from A (best) to E (worst).

14. Amtrak passenger trains are most often late in arriving at their destinations. Identify the potential error in arrival times as systematic or random. a.Systematic b.Random

15. Amtrak passenger trains are most often late in arriving at their destinations. Identify the potential error in arrival times as systematic or random. a.Systematic b.Random

16. A recipe for grape jelly calls for 4 pounds of grapes. The jelly maker estimates the 4 pounds of grapes by standing on a bathroom scale with and without the grapes. The scale only shows the weight to the nearest pound. Identify the error in the weight as systematic or random. a.Systematic b.Random

17. A recipe for grape jelly calls for 4 pounds of grapes. The jelly maker estimates the 4 pounds of grapes by standing on a bathroom scale with and without the grapes. The scale only shows the weight to the nearest pound. Identify the error in the weight as systematic or random. a.Systematic b.Random

18. A golfer estimates that the distance to the hole for his next shot is 58 yards. The actual distance is exactly 50 yards. What is the absolute error? a.8 yards b.– 8 yards c.16.0% d.–16.0%

19. A golfer estimates that the distance to the hole for his next shot is 58 yards. The actual distance is exactly 50 yards. What is the absolute error? a.8 yards b.– 8 yards c.16.0% d.–16.0%

20. Slide 2.3- 20Copyright © 2009 Pearson Education, Inc. Conversions Between Fractions and Percentages p. 68 To convert a percentage to a common fraction: Replace the % symbol with division by 100; simplify the fraction if necessary. Example: 25% = = To convert a percentage to a decimal: Drop the % symbol and move the decimal point two places to the left (that is, divide by 100). Example: 25% = 0.25 25 100 1414

21. Slide 2.3- 21Copyright © 2009 Pearson Education, Inc. Conversions Between Fractions and Percentages To convert a decimal to a percentage: Move the decimal point two places to the right (that is, multiply by 100) and add the % symbol. Example: 0.43 = 43% To convert a common fraction to a percentage: First convert the common fraction to a decimal; then convert the decimal to a percentage. Example: = 0.2 = 20% 1515

22. Convert 112.463% to decimal form. a.1.12463 b.11.2463 c.1124.63 d.11246.3

23. Convert 112.463% to decimal form. a.1.12463 b.11.2463 c.1124.63 d.11246.3

24. Convert 0.1963 to a percent. a.0.001963% b.0.01963% c.1.963% d.19.63%

25. Convert 0.1963 to a percent. a.0.001963% b.0.01963% c.1.963% d.19.63%

26. After a year of weight training, Harold’s weight changed from 172 pounds to 185 pounds. What is his percent increase in weight to the nearest tenth? a.13.0 pounds b.8.0% c.7.6% d.7.0%

27. After a year of weight training, Harold’s weight changed from 172 pounds to 185 pounds. What is his percent increase in weight to the nearest tenth? a.13.0 pounds b.8.0% c.7.6% d.7.0%

28. Slide 2.3- 28 Copyright © 2009 Pearson Education, Inc. Using Percentages to Describe Change Absolute and Relative Change – p. 69 The absolute change describes the actual increase or decrease from a reference value to a new value: absolute change = new value – reference value The relative change describes the size of the absolute change in comparison to the reference value and can be expressed as a percentage: relative change = × 100% new value – reference value reference value

29. Slide 2.3- 29 Copyright © 2009 Pearson Education, Inc. EXAMPLE 2 World Population Growth World population in 1950 was 2.6 billion. By the beginning of 2000, it had reached 6.0 billion. Describe the absolute and relative change in world population from 1950 to 2000. Solution: The reference value is the 1950 population of 2.6 billion and the new value is the 2000 population of 6.0 billion. absolute change = new value – reference value = 6.0 billion – 2.6 billion = 3.4 billion

30. Slide 2.3- 30 Copyright © 2009 Pearson Education, Inc. EXAMPLE 2 World Population Growth Solution: (cont.) relative change = × 100% = × 100% = 130.7% World population increased by 3.4 billion people, or by about 131%, from 1950 to 2000. new value – reference value reference value 6.0 billion – 2.6 billion 2.6 billion

31. Slide 2.3- 31 Copyright © 2009 Pearson Education, Inc. “Of” versus “More Than” (or “Less Than”) p. 71 If the new or compared value is P% more than the reference value, then it is (100 + P)% of the reference value. If the new or compared value is P% less than the reference value, then it is (100 - P)% of the reference value.

32. Slide 2.3- 32 Copyright © 2009 Pearson Education, Inc. EXAMPLE 4 World Population In Example 2, we found that world population in 2000 was about 131% more than world population in 1950. Express this change with an “of ” statement. Solution World population in 2000 was 131% more than world population in 1950. Because (100 + 131)% = 231%, the 2000 population was 231% of the 1950 population. This means that the 2000 population was 2.31 times the 1950 population.

33. Common Roots  Comparisons must be made within the same unit of measure.  Create a common root before making comparisons  Watch for decimals and place holders Teach Back: Absolute and relative differences Per Capita GDP: Ivory-US (each) GDP: Ivory-US Population: Ivory-US Hourly min. wage: Ivory-US BONUS: Create a comparison with the US V-Day chocolate data. http://thecnnfreedomproject.blogs.cnn.com/2012/01/17/who-consumes-the-most-chocolate/