Transcript Communicating Quantitative Information

Communicating Quantitative
Information
Normal distribution
Values, changes, changes of changes
Female/Male income.
Questions on Midterm
Homework: prepare for midterm.
(Post project I proposal)
Normal distribution
Aka bell shaped curve
• Distribution: horizontal axis different values,
vertical axis, number of incidents of that value
• Mean = mode= median
• and specific falling away from
mean/mode/median
– Much less (fewer?) incidence of values away from the
mean/mode/median. These are also called outliers
– Exact description is given in terms of standard
deviation. Square root of (1/N * Sum(xi-mean)2)
(continuous) normal curve
34.1%
Red area = 68.2% of total
Red+green = 95.4%
Red + green + blue (6 sigma)
= 99.6%
1 standard
deviation
Why is normal important
• Empirically, many things in nature appear
to exhibit this type of distribution
• Mathematically, binomial → normal
What does this mean? Remember coin
tossing:
Probabilities of 0, 1, 2 heads in tossing coin
2 times is: 1/4, 2/4, 2/4, 1/4
Probabilities of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
heads in tossing coin 10 times is:
0
1E-03
1
2
0.01 0.044
3
4
5
6
0.117 0.205 0.246 0.205
7
8
0.117 0.044
9
10
0.01 1E-03
Note: 1E-03 means 1 times 10 raised
to the negative 3 power means .001
Notice: numbers falling off from
center.
Normal
• So, if a condition/value is the result of
many different more or less on and off
effects (binomial = 2 things), then
cumulative effect is to be normal….
Graphs
• What graph and/or diagram and/or picture
reveals the important aspects of the story?
• Pie is for parts of a whole
• Bar is for comparing things or sets of things or
…
• Line graph generally used when the underlying
phenomenon has continuous nature
• For bar or for line, time is frequent variable,
generally on the horizontal axis.
Change
• Dental expense and inflation showed
change, NOT underlying values
• Can show change over time
• Can show change of change
These ideas are familiar to you!
• Think of velocity of car
change in position / change in time
• Acceleration
change in velocity / change in time
Women wages vs Men wages
• Say, John Smith made $100,000 and Jane
Doe made $117,000….then Jane made
17% more than John.
– John's salary is the base
• But, they're talking about group of women
and group of men
• They decided to use median as their
'measure of centrality'.
Women/Men wages, cont.
• Case 1:
– 5 men making
30000 30000 100000 100000 200000
MEDIAN is 100000
Mean (aka average) = 92000
– 3 women making
30000 117000 200000
MEDIAN is 117000
Mean =115666.67
Using medians or means, these women making
more than these men!!!
Women/Men wages, cont.
• Case 2:
– 5 men making
30000 30000 100000 100000 1000000
MEDIAN is 100000
Mean (aka average) = 252000
– 3 women making
30000 117000 200000
MEDIAN is 117000
Mean =115666.67
In this case, women are ahead if using medians,
men ahead if using means.
Mean vs Median issue?
• No, in conversations with the researcher,
the mean vs median would not have
changed the result
– This population of women were making more
than the men by either measure
• However, the real news was the
composition of each group.
Women/Men, cont.
• Schematic of actual case
– Men in two groups, MH (men high school) and MC
(men with college degree). More MH then MC.
– Women in two groups, WH and WC, more WC than
WH.
– Mean or Median
WH < MH < WC < MC
Because the median (or the mean) of the Men tends
more to that measure of the MH and the median (or
the mean) of the Women tends to that of the WC, the
total has women outearning men!
It actually is something like case 2 with the one very
high earning man!
New York Times article
• Graph included ethnic break down that
was confusing if you tried to 'do arithmetic'
because you can't do this with medians.
• Look at our postings and re-read article!
Presentation: graphs and diagrams
• Communication issue
• Consider
–
–
–
–
Stock market
Polls
Health, development issues
?
• Recall 5 D's
– Chart should show 'what is the difference' and
distribution and dimension
– May or may not show denominator
– Need to check definition(s)
Midterm
• Your questions?