Introduction to descriptive statistics
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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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Skewness symmetrical distribution l.jpg
SkewnessSymmetrical distribution

  • IQ

  • SAT


Skewness asymmetrical distribution l.jpg
SkewnessAsymmetrical distribution

  • GPA of MIT students


Skewness asymmetrical distribution11 l.jpg
Skewness(Asymmetrical distribution)

  • Income

  • Contribution to candidates

  • Populations of countries

  • “Residual vote” rates





A few words about the normal curve l.jpg
A few words about the normal curve

  • Skewness = 0

  • Kurtosis = 3






Commands in stat for getting univariate statistics l.jpg
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 l.jpg
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 l.jpg
Graph Q9

. graph q9


Divide into 7 bins and have them span 1 1 2 2 3 6 7 l.jpg
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 l.jpg
Add ticks at each integer score … 6..7

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


Add a finer grain to the bars l.jpg
Add a finer grain to the bars … 6..7

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


Even finer grain l.jpg
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 with the same mean and s d as the empirical distribution l.jpg
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


Do the previous graph with only larger classes n 20 l.jpg
Do the previous graph with only larger classes (n > 20) … 6..7

. 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 l.jpg
Draw the previous graph with a box plot … 6..7

. graph q9 if n>20,box ylabel


Draw the box plots for small 0 20 medium 21 50 and large 50 classes l.jpg
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 l.jpg
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 l.jpg
Simple graph large (50+) classes


Solution step 1 map artificial category onto natural midpoint l.jpg
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 l.jpg
Graph of recoded data large (50+) classes


Density plot of data l.jpg
Density plot of data large (50+) classes


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