Communicating Quantitative Information

Normal distributionValues, 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 → normalWhat 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 1 2 3 4 5 6 7 8 9 10

1E-03 0.01 0.044 0.117 0.205 0.246 0.205 0.117 0.044 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 changeThese 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 200000MEDIAN is 100000Mean (aka average) = 92000

– 3 women making30000 117000 200000 MEDIAN is 117000Mean =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 1000000MEDIAN is 100000Mean (aka average) = 252000

– 3 women making30000 117000 200000 MEDIAN is 117000Mean =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 < MCBecause 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?