Statistical Reasoning for everyday life Intro to Probability and Statistics Mr. Spering – Room 113

2.3 Uses and Abuses of Percentages Remember a fraction is a decimal is a percent. Recall these fractions:

2.3 Uses and Abuses of Percentages CHANGES: Reference value (starting number) & New value Absolute change – describes the actual increase or decrease from a reference value to a new value: absolute change = new value – reference Relative change – describes the size of the change in comparison to the reference value and can be expressed as a percentage relative change = new value – reference value X 100% reference value

2.3 Uses and Abuses of Percentages  DIFFERENCES: Reference value (basis for comparison) & compared value (compare to the reference) Absolute difference – describes the actual amount by which the compared value is larger or smaller than the reference absolute difference = compared – reference Relative difference – describes the size of the difference as a percentage Relative difference = compare – reference X 100% reference

2.3 Uses and Abuses of Percentages “of” versus “more than” {process of referencing the new value and original value} If the compared value is P% more than the reference value, then it is (100 +P)% of the reference value. Similarly, if the compared value is P% less than the reference value, then (100 – P)% of the reference value.

2.3 Uses and Abuses of Percentages Example: Absolute change & Relative change 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. 1. Absolute change = new – reference = 6 – 2.6 = 3.4 billion increase 2. Relative change = new – reference X 100% reference = 6 – 2.6 X 100% 2.6 = 130 % increase

2.3 Uses and Abuses of Percentages Example: Absolute difference & Relative differences Life expectancy of American men is about 73 years, while the life expectancy for Russian men is about 59 years old. Compare the life expectancy of American men to that of Russian men. 1. Absolute difference = compared – reference = 73 – 59 = 14 years greater 2. Relative difference = compared – reference X 100% reference = 73 – 59 X 100% 59 = 24 % greater

2.3 Uses and Abuses of Percentages Example: “of” versus “more than”  Consider a population that triples in size from 200 to 600:  Using “more than”: The new population is 200% more than the original.  Using “of”: The new population is 300% of the original. (percent increase or decrease)

2.3 Uses and Abuses of Percentages How the mathematical language confuses? Take care in wording! “percentage points” versus “%”  When a change is expressed as a percentage point, assume it is an absolute change or difference. If a change is expressed with the % symbol or the word percent it is a relative change or difference.

2.3 Uses and Abuses of Percentages

Find the absolute and relative values for the situation: The number of daily newspapers in the United States was 2,226 in 1900 and 1,509 in Absolute change: 717 decline Relative change: 32.2% decline

2.3 Uses and Abuses of Percentages Find the absolute and relative values for the situation: When purchasing DVD’s some cost $20 and others cost $12. Compare the more expensive DVD’s to the less expensive. Absolute difference: $20 DVD’s are $8 greater Relative difference: $20 DVD’s are 67% more expensive

2.3 Uses and Abuses of Percentages Take care in wording: Assume 40% of the registered voters in Carson City are Republicans. a) The percentage of voters registered as Republicans is 25% higher in Freetown than in Carson City. What percentage of the registered voters in Freetown are Republicans? 50% b) The percentage of voters registered as Republicans is 25 percentage points higher in Freetown than in Carson City. What percentage of the registered voters in Freetown are Republicans? 65% HW #9 pg 73 # 6-34 even