Transcript Statistical Reasoning - Palisades High School

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.
1
 0.25  25%
4
Recall these fractions:
1 1 1 1 1 1 1
1
, , , , , , ,&
2 3 4 5 6 8 9 10
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
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 1997.
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