Chapter 3
• 3-A Uses and Abuses of Percentages
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Shopping at KOHL’S
$24.00 item is 25% Off
30% additional coupon
Do you get 55% off?
Theory
• Entices the buyer to think that they will get
55% off.
• Reality is you don’t get 55% off, you actually
get 52.5%
Math
• $24.00 – 25% = $6.00 off =$18.00
• $18.00 – 30% = $5.40 off = $12.60 total cost
• 12.60 / 24.00 = 52.5% Actual Percentage
Mathematical Confusion
• 55% - 52.5% = 2.5% difference
• $24.00 – 55% = $13.20 total off
• $24.00 – $13.20 = $10.80 total cost
• 2.5% difference = $1.80
• Shoppers Beware!!!
3 –B Putting Numbers in Perspective
Perspective
• Scaling
• Verbal- Graphical- Ratio Scaling
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Ratio Scaling
Miles across America from LA to Boston
Miles = 3037
Scale – 1 mile = 11 inches
Ratio- 1:5760 in real life inches
Map
• There are 3037 miles from LA to Boston
• If we use a Matchbox car how far will it travel
from Taylorsville Campus down Redwood
Road?
1mile 5280ft 12inches = 63,360 inches
1mile 1 foot
63,360 inches
= 1 : 5,760 ratio
11 inches
Math
3037 miles X 11 inches = 33,407 inches
33,407 inches X
1 mile
= .527 miles
63,360 inches
This would be from :
• From Taylorsville Campus to Taylorsville Park
with a 2” Matchbox car.
Dealing with Uncertainty
• Accuracy- How close a number is to its True
Value
• Precision- How close it is to the amount of
correct significant digits
Example
• Worker at a Coffee Packaging Plant, have two
scales to measure the amount of coffee put
into each package.
• Scale 1 reads - .56 kg
• Scale 2 reads - .6 kg
• Actual weight = .65 kg
Explanation
• Which scale is most precise and
which is more accurate?
• Scale 1 is more precise because it reads up to
2 sig. digits.
• Scale 2 is more accurate because it reads to
the closest true value.
3 – E Deceiving Numbers
Lived
Died
Total
% lived
(cir.
2000)
Lived
Died
Total
% lived
(cir.
2010)
Mercy
1190
Hospital
310
1500
79%
815
385
1200
68%
County 770
Hospital
230
1000
77%
700
300
1000
70%
Multiplying Percentages
• Mercy Hospital is .79 X .68 = .5372
• County Hospital is .77 X .7 = .539
This shows County Hospital is better!
Yet- This is NOT true
Simpson’s Paradox
Multiplying Percentages doesn’t work because they
are representations of ratios not actual numbers
1190 + 815 = 2005 /2700 = .7425
770 +700 = 1470 / 2000 = .735
• These are the actual Percentages of the people
that lived for both years.
• Mercy Hospital total = 74.3%
• County Hospital total = 73.5%
Comparison
• When we multiplied the percentages
together we found that County Hospital was
slightly better than Mercy Hospital
• The reality is that Mercy Hospital is better at
helping people live!
• This is Simpson’s Paradox