Bài giảng tối ưu hóa Bài 5 Basic concept statistics Ph.D Lê Minh Tâm

Variable Variable Variable Variable Variable Variable Variable Variable Variable 5/21/2019... Difference Order SimilarInterval Meaningful zero point Categorical... Categorical vari

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Variable

Variable

Variable

Variable Variable

Variable

Variable

Variable Variable

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Difference Order Similar

Interval

Meaningful zero point Categorical

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Job Frequency Relative freq

?

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Categorical variable

Quantitative variable

Frequency table

Pie chart Bar graph

Dot plot Histogram Distribution

× 100

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× 586

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Bell shaped Skewed to the right

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Categorical variable

Quantitative variable

Mode

Mean Median

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The average monthly salary of a couple ?

?

x x x x

x x x

x

x

x x

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Mode = 38.5 ; Median = 39.2 ; Mean = 39.3

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Q1 Q2 Q3 25%

25% 25%

25%

Q1 Q2 Q3 Q1 – 1.5 * IQR

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Q2 IQR

Q3 Min (Maximum value in the data, Q3 + 1.5* IQR)

Max (Minimum value in the data, Q1 - 1.5* IQR)

Outlier

The variability within the two distributions strongly differs

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Group 2

> var(group1) [1] 12.252

> sd(group1) [1] 3.500286

> var(group2) [1] 0.714

> sd(group2) [1] 0.8449852

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- z-score Mom1 32.7 -6.6 -1.89

Original values are above the mean

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95%

99%

exceptional exceptional

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Skewed to the right Skewed to the left

More extreme values

Large positive

z-score

Large negative

z-score

89%

exceptional exceptional

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Compute z-score when =41 ?

Compute z-score when =41 ?

;

Group 2

For conclusion, you can say that

41 weeks of the the baby's gestational age happens more common in Group 1 than in Group 2

More extent …

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Focus on the average grade for Math+, from 0 to 10, we want to know some information :

1 What does the distribution (of the variable) look like ?

2 What is the central tendency of the distribution ?

3 What is the dispersion of the distribution ?

4 What does the box plot look like ?

5 Compute the z-score of the school #3, what story does it

tell you ?

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Average grade School 1 7.4

School 2 7.9 School 3 4.1 School 4 8.1 School 5 6.2 School 6 7.1 School 7 7.4

Outlier ?!

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4.1 6.2 6.7 7.1 7.4 7.4 7.9 8.1

Sorting

data

Range = 4.0 IQR = 1.2 sd =1.27

First: warning outlier !!!