MEASURES OF CENTRALITY

Last lecture summary• Which graphs did we meet?

• scatter plot (bodový graf)• bar chart (sloupcový graf)• histogram• pie chart (koláčový graf)

• How do they work, what are their advantages and/or disadvantages?

Random noise

SIZE [ft2] COST [$]1 300 88 0001 400 72 0001 600 94 0001 900 86 0002 100 112 0002 300 98 000

Histogram• Now I will collect heights of all of you in this room.

• Use Interactive Histogram Applet: http://www.shodor.org/interactivate/activities/Histogram/

• interval, bin

Histogram – Body fat• In Interactive Histogram Applet – choose „Body fat % in 252 men“

dataset.• Find reasonable bin size• Answer following questions. No matter of bin size what is always

true?

• Most scores fall around 20%.• The shape is roughly symmetrical.• Most scores fall in the middle of distribution.• There are more scores between 15 and 25 than between 35 and

50.• There are more scores between 0 and 10 than between 18 and 24.• Relatively more men have a body fat above 35% or below 5%.

Histogram – Income distribution• United States Census Bureau – http://www.census.gov

Income Number of houses10 000 9401

20 000 14447

30 000 13642

40 000 12388

50 000 11028

Histogram – Income distribution

• This is an example of a (positively) skewed distribution (zprava zešikmené rozdělení).

• This distribution is not symmetrical.

• Most incomes fall to the left of the distribution.

Bar chart and scatter plot• Which scatter plot corresponds to this bar chart?

Pie chart to histogram• Which histogram looks like it cames from the same data?

About statistics• Statistics – the science of collecting, organizing,

summaryzing, analyzing, and interpreting data• Goal – use imperfect information (our data) to infer facts,

make predictions, and make decisions

• Descriptive statistic – summarising data with numbers or pictures

• Inferential statistics – making conclusions or decisions based on data

Choosing a profession

Chemistry Geography

50 000 – 60 000 40 000 – 55 000

Choosing a profession• We made an interval estimate.• But ideally we want one number that describes the entire

dataset. This allows us to quickly summarize all our data.

Choosing a profession

1. The value at which frequency is highest.2. The value where frequency is lowest.3. Value in the middle.4. Biggest value o x-axis.5. Mean

Chemistry Geography

Three big M’s

• The value at which frequency is highest is called the mode. i.e. the most common value is the mode.

• The value in the middle of the distribution is called the median.

• The mean is the mean.

Chemistry Geography

Quick quiz• What is the mode in our data?

Mode in negatively skewed distribution

Mode in uniform distribution

Multimodal distribution

Mode in categorical data

More of modeTrue or False?

1. The mode can be used to describe any type of data we have, whether it’s numerical or categorical.

2. All scores in the dataset affect the mode.3. If we take a lot of samples from the same population, the mode will be

the same in each sample.4. There is an equation for the mode.

• Ad 3.• http://onlinestatbook.com/stat_sim/sampling_dist/ • Mode changes as you change a bin size.

• The mode depends on how you present data. And we can’t use mode to learn something about our population.

Life expectancy data• Watch TED talk by Hans Rosling, Gapminder Foundation:

http://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen.html