1. Measures of Central Tendency

  • Statistic (ํ†ต๊ณ„๋Ÿ‰) & Parameter (๋ชจ์ˆ˜)
    • ํ†ต๊ณ„๋Ÿ‰ : sample(ํ‘œ๋ณธ)์˜ ๋ฐ์ดํ„ฐ ๊ฐ’์„ ์‚ฌ์šฉํ•˜์—ฌ ์–ป์€ ํŠน์„ฑ ๋˜๋Š” ์ธก์ •๊ฐ’
    • ๋ชจ์ˆ˜ : ํŠน์ • population(๋ชจ์ง‘๋‹จ)์˜ ๋ชจ๋“  ๋ฐ์ดํ„ฐ ๊ฐ’์„ ์‚ฌ์šฉํ•˜์—ฌ ์–ป์€ ํŠน์„ฑ ๋˜๋Š” ์ธก์ •๊ฐ’

Mean

Median

: halfway point, midpoint
โ†’ 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
โ†’ Outlier ์žˆ๋‹ค๋ฉด?

Weighted mean

k% trimmed mean
: ์ž‘์€๊ฑฐ์—์„œ k%, ํฐ๊ฑฐ์—์„œ k% ๋นผ๊ณ  100-2k%๋กœ๋งŒ ํ‰๊ท ์„ ๊ณ„์‚ฐ

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

2. Measures of Variation

Range


Population variance and standard deviation


Sample variance and standard deviation

  • basic formulas
  • short-cut formulas

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


Coefficient of variation (๋ณ€๋™๊ณ„์ˆ˜)

โ†’ ๋น„๊ต๋‹จ์œ„๊ฐ€ ๋‹ค๋ฅด๊ธฐ ๋•Œ๋ฌธ์—


Range rule for thumb

Be used to approximate the standard deviation


Chebyshevโ€™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

3. Measures of Position

Standard scores ( ํ‘œ์ค€์ ์ˆ˜ )

โ†’ ํ‘œ์ค€์ ์ˆ˜๋Š” ๋ฐ์ดํ„ฐ ๊ฐ’์ด ํ‰๊ท ๋ณด๋‹ค ๋†’๊ฑฐ๋‚˜ ๋‚ฎ์€ ํ‘œ์ค€ ํŽธ์ฐจ์˜ ์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค


Percentiles ( ๋ฐฑ๋ถ„์œ„์ˆ˜ )

โ†’ ์ด๋Ÿฌํ•œ ๊ฐ ๋ถ€๋ถ„์—๋Š” ์ฆ๊ฐ€ํ•˜๋Š” ์ˆœ์„œ๋กœ ๋ฐฐ์—ด๋œ ๋ฐ์ดํ„ฐ ์ง‘ํ•ฉ์˜ ๊ด€์ธก๊ฐ’ ์ค‘ 1%๊ฐ€ ํฌํ•จ


Quartiles ( ์‚ฌ๋ถ„์œ„์ˆ˜ )

IQR ( Interquarile Range )

IQR=Q3โˆ’Q1IQR = Q_3 - Q_1


Outlier ( ์ด์ƒ๊ฐ’ )


Exploratory Data Analysis (EDA)

  • 5-number summary & Boxplots
    • min, ๐‘„1๐‘„_1, ๐‘„2๐‘„_2 , ๐‘„3๐‘„_3 , max

  • Ex_
    75 69 84 112 74 104 81 90 94 144 79 98
    Construct a box-and-whisker plot for these data.

HGU GLSํ•™๋ถ€ ๊น€ํ—Œ์ฃผ ๊ต์ˆ˜๋‹˜์˜ 23-2 ํ†ต๊ณ„ํ•™ ์ˆ˜์—…์„ ๋“ฃ๊ณ  ์ž‘์„ฑํ•œ ํฌ์ŠคํŠธ์ด๋ฉฐ, ์ฒจ๋ถ€ํ•œ ๋ชจ๋“  ์‚ฌ์ง„์€ ๊ต์ˆ˜๋‹˜ ์ˆ˜์—… PPT์˜ ์‚ฌ์ง„ ์›๋ณธ์— ํ•„๊ธฐ๋ฅผ ํ•œ ์ˆ˜์ •๋ณธ์ž…๋‹ˆ๋‹ค.

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