[ Statistics ] 03. Data Description

1. Measures of Central Tendency

• Statistic (통계량) & Parameter (모수)
  • 통계량 : sample(표본)의 데이터 값을 사용하여 얻은 특성 또는 측정값
  • 모수 : 특정 population(모집단)의 모든 데이터 값을 사용하여 얻은 특성 또는 측정값

Mean

Median

: halfway point, midpoint
→ Exist outlier : median > mean

Mode

: Most often

Unimodal : only one mode
Bimodal : two modes
Multimodal : more than two modes

Midrange

: rough estimate of the middle
→ Outlier 있다면?

Weighted mean

k% trimmed mean
: 작은거에서 k%, 큰거에서 k% 빼고 100-2k%로만 평균을 계산

Properties and uses of central tendency

• Relationships among the mean, median, and mode
  • for a symmetric histogram
  • skewed to the right
  • skewed to the left

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2. Measures of Variation

Range

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Population variance and standard deviation

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Sample variance and standard deviation

• basic formulas
• short-cut formulas

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Variance and standard deviation for grouped data

Similar for finding the mean for grouped data

Ex_
The data represent the # of miles that 20 runners ran during one week

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Coefficient of variation (변동계수)

→ 비교단위가 다르기 때문에

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Range rule for thumb

Be used to approximate the standard deviation

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Chebyshev’s theorem

Ex_

The empirical (normal) rule

• For a bell shaped distribution, approximately
  • 68% of the obs. lie within 1 std. of mean
  • 95% of the obs. lie within 2 std. of mean
  • 99.7% of the obs. lie within 3 std. of mean

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3. Measures of Position

Standard scores ( 표준점수 )

→ 표준점수는 데이터 값이 평균보다 높거나 낮은 표준 편차의 수를 나타낸다

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Percentiles ( 백분위수 )

→ 이러한 각 부분에는 증가하는 순서로 배열된 데이터 집합의 관측값 중 1%가 포함

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Quartiles ( 사분위수 )

IQR ( Interquarile Range )

$IQR = Q_3 - Q_1$

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Outlier ( 이상값 )

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Exploratory Data Analysis (EDA)

• 5-number summary & Boxplots
  • min, $𝑄_1$, $𝑄_2$ , $𝑄_3$ , max
    
    
• Ex_
  75 69 84 112 74 104 81 90 94 144 79 98
  Construct a box-and-whisker plot for these data.
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HGU GLS학부 김헌주 교수님의 23-2 통계학 수업을 듣고 작성한 포스트이며, 첨부한 모든 사진은 교수님 수업 PPT의 사진 원본에 필기를 한 수정본입니다.