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## PowerPoint Slideshow about 'Introduction to Descriptive Statistics' - johana

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SkewnessAsymmetrical distribution

- GPA of MIT students

Skewness(Asymmetrical distribution)

- Income
- Contribution to candidates
- Populations of countries
- “Residual vote” rates

A few words about the normal curve

- Skewness = 0
- Kurtosis = 3

Commands in STAT for getting univariate statistics

- summarize
- summarize, detail
- graph, bin() normal
- graph, box
- tabulate [NB: compare to table]

Explore Q9: Overall teaching evaluation

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

Divide into 7 “bins” and have them span 1, 1..2, 2..3, … 6..7

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

Add ticks at each integer score

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

Add a finer grain to the bars

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

Even finer grain

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

Superimpose the normal curve (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

Do the previous graph with only larger classes (n > 20)

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

Draw the previous graph with a box plot

. 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

(196 real changes made)

. replace size = 2 if n > 100

(41 real changes made)

. sort size

. graph q9 ,box ylabel by(size)

. graph q9 ,box ylabel by(size)

A note about histograms with unnatural categories

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

Solution, Step 1Map 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)

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