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# Introduction to Descriptive Statistics - PowerPoint PPT Presentation

Introduction to Descriptive Statistics. 2/25/03. Population vs. Sample Notation. Types of Variables. Describing data. Mean. Variance, Standard Deviation. Variance, S.D. of a Sample. Coefficient of variation. Skewness Symmetrical distribution. IQ SAT. Skewness Asymmetrical distribution.

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### Introduction to Descriptive Statistics

2/25/03

SkewnessSymmetrical distribution

• IQ

• SAT

SkewnessAsymmetrical distribution

• GPA of MIT students

Skewness(Asymmetrical distribution)

• Income

• Contribution to candidates

• Populations of countries

• “Residual vote” rates

• Skewness = 0

• Kurtosis = 3

• summarize

• summarize, detail

• graph, bin() normal

• graph, box

• tabulate [NB: compare to table]

subject q9 n

3.371 6.4375 16

3.982 6.73333 15

3.14 6.46154 13

14.02D 5.66667 3

21W.803 5.66667 12

21M.480 5.69231 13

17.906 5.28571 14

2.51 5.88235 17

. graph q9

. graph q9,bin(7) xscale(0,7)

. graph q9,bin(7) xscale(0,7) xlabel(0,1,2,3,4,5,6,7)

. graph q9,bin(14) xscale(0,7) xlabel(0,1,2,3,4,5,6,7)

Even finer grain … 6..7

• . graph q9,bin(28) xscale(0,7) xlabel(0,1,2,3,4,5,6,7)

Superimpose the normal curve … 6..7(with the same mean and s.d. as the empirical distribution)

. graph q9,bin(28) xscale(0,7) xlabel(0,1,2,3,4,5,6,7) norm

. graph q9 if n>20,bin(28) xscale(0,7) xlabel(0,1,2,3,4,5,6,7)

. graph q9 if n>20,box ylabel

Draw the box plots for small (0..20), medium (21..50), and large (50+) classes

. gen size = 0 if n <=20

(237 missing values generated)

. replace size=1 if n > 20 & n <=100

. replace size = 2 if n > 100

. sort size

. graph q9 ,box ylabel by(size)

. graph q9 ,box ylabel by(size)

A note about histograms with unnatural categories large (50+) classes

From the Current Population Survey (2000), Voter and Registration Survey

How long (have you/has name) lived at this address?

-9 No Response

-3 Refused

-2 Don't know

-1 Not in universe

1 Less than 1 month

2 1-6 months

3 7-11 months

4 1-2 years

5 3-4 years

6 5 years or longer

Simple graph large (50+) classes

Solution, Step 1 large (50+) classesMap artificial category onto “natural” midpoint

-9 No Response  missing

-3 Refused  missing

-2 Don't know  missing

-1 Not in universe  missing

1 Less than 1 month  1/24 = 0.042

2 1-6 months  3.5/12 = 0.29

3 7-11 months  9/12 = 0.75

4 1-2 years  1.5

5 3-4 years  3.5

6 5 years or longer  10 (arbitrary)

Graph of recoded data large (50+) classes

Density plot of data large (50+) classes