This document discusses descriptive statistics concepts like sorting, ranking, percentiles, and comparisons using GDP data. It explains how sorting data makes it easy to find things like the richest and poorest countries. Percentiles allow comparisons across groups by expressing an observation as a percentage. For example, the US GDP percentile was 94.5% in 1980. Grouping can be done based on percentiles, like the top 10% of countries. However, comparisons are always subjective since the group, benchmark, and criteria can be manipulated.

2. Intro to Stats forIntro to Stats for
MuslimsMuslims
Unit 02: DescriptiveUnit 02: Descriptive
StatisticsStatistics
Lecture 2:Lecture 2:
Comparisons:Comparisons:
Sorting, Ranking, PercentilesSorting, Ranking, Percentiles

3. Comparisons: Always SubjectiveComparisons: Always Subjective
Sheikh Saadi: Story of boy who did not get newSheikh Saadi: Story of boy who did not get new
shoes for Eid.shoes for Eid.
 What is the benchmark for comparisons?What is the benchmark for comparisons?
 What is the criterion for comparisons?What is the criterion for comparisons?
 Why are comparisons being made?Why are comparisons being made?

4. Numbers are clues to realityNumbers are clues to reality
 Every fact about numbers provides someEvery fact about numbers provides some
information about the real world.information about the real world.
 We must know the meaning of the numbersWe must know the meaning of the numbers
to understand what information is provided.to understand what information is provided.
 Conventional statistics deals with numbersConventional statistics deals with numbers
onlyonly
 IS deals with meanings of numbers – theIS deals with meanings of numbers – the
relation to the real world. It is this meaningrelation to the real world. It is this meaning
which allows us to make arguments/rhetoricwhich allows us to make arguments/rhetoric

5. GNP per capita: in PPP constantGNP per capita: in PPP constant
2000$2000$
 If all market earnings in PKR wereIf all market earnings in PKR were
converted to USD at PPP exchange rates,converted to USD at PPP exchange rates,
and divided equally, everyone would haveand divided equally, everyone would have
USD 461 in inflation adjusted 2000 dollars.USD 461 in inflation adjusted 2000 dollars.
 China was slightly behind Pakistan in 1990 inChina was slightly behind Pakistan in 1990 in
terms of this measure, but forgedterms of this measure, but forged
significantly ahead during the decade.significantly ahead during the decade.
Country GDP 1990 GDP 2000
China 391.65 949.18
Pakistan 461.40 531.00

6. Sorting the DataSorting the Data

 Look atLook at
Spreadsheet.Spreadsheet.
 UNSORTED data.UNSORTED data.
 Rank of Pakistan?Rank of Pakistan?
 Richest countries?Richest countries?
 Poorest countries?Poorest countries?
 After SORTING,After SORTING,
it becomes EASYit becomes EASY
to answer theseto answer these
questions just byquestions just by
looking at the list.
Country 2010
Algeria 2232
Bangladesh 558
Bermuda 63036
Chad 300
China 2427
Congo 106
Cuba 4495
Ethiopia 219
India 804
Indonesia 1145
LDC (UN class) 395
Morocco 1844
Pakistan 665
Saudi Arabia 9499
Spain 15419
Sri Lanka 1309
Turkey 5356

7. Spreadsheet ConceptsSpreadsheet Concepts
Lab Work [not covered in lecture]Lab Work [not covered in lecture]
 Search for, find, download WDI Data SetSearch for, find, download WDI Data Set
 Learn how to extract relevant information.Learn how to extract relevant information.
 Create new spreadsheet with desired info.Create new spreadsheet with desired info.
 SORT according to desired criterionSORT according to desired criterion
 Lecture covers Use and Meaning.Lecture covers Use and Meaning.
 TERMS: Maximum, Minimum, Rank, RangeTERMS: Maximum, Minimum, Rank, Range

8. Country Name 1980 1990 2000 2010
Congo, 779 631 260 316
Liberia 1263 355 344 488
Burundi 604 689 496 524
Niger 941 702 597 650
Cen African Rep 994 853 759 706
Malawi 691 572 670 780
Mozambique 435 396 501 823
United States 25510 31899 39545 42079
U A Emirates 123263 73502 69078 42353
Hong Kong 14118 24019 30290 42581
Brunei 80588 50393 48478 45507
Norway 26205 32362 43975 46906
Singapore 15116 25234 38063 52170
Luxembourg 27622 42707 61091 68679
MIN 435 355 260 316
MAX 123263 73502 69078 68679
RANGE 122828 73146 68818 68362

9. Outliers: Qatar, Kuwait, Brunei,UAEOutliers: Qatar, Kuwait, Brunei,UAE
0
2 0 0 0 0
4 0 0 0 0
6 0 0 0 0
8 0 0 0 0
1 0 0 0 0 0
1 2 0 0 0 0
1 4 0 0 0 0
1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5
R a n g e w it h o u t o u t lie r s

10. RANKING
Country Name 1980 1990 2000 2010
Congo. 121 127 130 130
Liberia 104 130 129 129
Burundi 127 124 128 128
Niger 114 123 126 127
Cent Afric Rep 111 118 120 126
Malawi 123 128 124 125
Mozambique 130 129 127 124
Madagascar 103 112 118 123
Switzerland 4 4 7 8
United States 8 6 5 7
U A Emirates 1 1 1 6
Hong Kong 31 19 16 5
Brunei 2 2 3 4
Norway 6 5 4 3
Singapore 29 15 6 2
Luxembourg 5 3 2 1

11. Comparing across groups
Group Size = N.
PERCENTILE: (N-Rank)/N
Example: 70, 75, 85, 95, 99 N=5
69: 0% 70 71: 20%
74: 20% 75 76: 40%
ALLOWS for comparisons across groups.
HOWEVER, Quiz toughness, Student IQ and
other factors not considered.

12. Percentile Graph: ECDF

13. Percentiles
Country 1980 1990 2000 2010
Congo. 6.9% 2.3% 0.0% 0.0%
Liberia 20.1% 0.0% 0.8% 0.8%
Burundi 2.3% 4.6% 1.5% 1.5%
Niger 12.4% 5.4% 3.1% 2.3%
C Afric Rep 14.7% 9.3% 7.7% 3.1%
Malawi 5.4% 1.5% 4.6% 3.8%
Mozambiqu
e
0.0% 0.7% 2.3% 4.6%
Madagascar 20.9% 13.9% 9.3% 5.4%
Switzerland 97.6% 97.6% 95.3% 94.5%
U S A 94.5% 96.1% 96.8% 95.3%
U A Emirates 100% 100% 100% 96.1%
Hong Kong 76.7% 86.0% 88.3% 96.8%
Brunei 99.2% 99.2% 98.4% 97.6%
Norway 96.1% 96.8% 97.6% 98.4%
Singapore 78.2% 89.1% 96.1% 99.2%

14. ECDF or Percentile Graph forECDF or Percentile Graph for
GDPGDP

15. Grouping according to PercentilesGrouping according to Percentiles
 Top 10% countries.Top 10% countries.
 Top Quarter = Third QuartileTop Quarter = Third Quartile
 Top Half = Above Median.Top Half = Above Median.
 Bottom Quarter = First Quartile.Bottom Quarter = First Quartile.
 Qualitative labels like: poor, rich, middleQualitative labels like: poor, rich, middle
income are based on these, but subjective.income are based on these, but subjective.

16. Review of Technical TermsReview of Technical Terms
 Minimum, Maximum, RangeMinimum, Maximum, Range
 Ranks and PercentilesRanks and Percentiles
 Median, Quartiles, QuintilesMedian, Quartiles, Quintiles
 New Term: Inter-Quartile Range (IQR)New Term: Inter-Quartile Range (IQR)
Exercises will give you practice on use andExercises will give you practice on use and
calculation of these terms.calculation of these terms.

17. RhetoricRhetoric
 Sorting and Ranking used for comparions.Sorting and Ranking used for comparions.
 Data/facts Objective BUT actuallyData/facts Objective BUT actually
subjective:subjective:
 Choose Group (take only African countries)Choose Group (take only African countries)
 Choose Benchmark. BETTER than who?Choose Benchmark. BETTER than who?
 Choose Criterion. HDI instead of GNPChoose Criterion. HDI instead of GNP
 Happiness/Welfare instead of Wealth.Happiness/Welfare instead of Wealth.