Chap 3. 자료의 정리(II)


3.1 서론


3.2 중심위치의 측도 (measures of central tendency)
  • Population mean : \mu
  • Sample mean :
    • arithematic mean : \bar x = \sum_{i=0}^n {x_i / n}
    • geometric mean : G=(x_1 x_2 ... x_n)^{1/n}
    • harmonic mean : H=n/{\sum_{i=0}^n 1/x_i}

  • Sample median : \tilde x
    • single middle value in the ordered list if n is odd
    • the average of the two middle values in the ordered list if n is even

  • mode : the greatest frequency value
  • Trimmed mean : \bar x_{tr(5)}
    • eliminating the smallest 5% and the largest 5% of the sample and then averaging what is left over.


3.3 산포도 (Measures of Variability)

  • population variance : \sigma^2 = {1 \over N} {\sum_{i=1}^N (x_i - \mu )^2}
  • population standard deviation : \sigma
  • sample variance : s^2={1 \over n-1} {\sum_{i=1}^n (x_i - \bar x )^2} <LI> sample standard deviation : <img src=
  • coefficient of variation : v={s \over \bar x}
  • range : Y_n - Y_1 where, Y_1:minimum value, Y_n:maximum value.
  • After the n observations in a data set are ordered from smallest to largest, the lower fourth and upper fourth are given by
    • Q_1 Lower quartile = median of the smallest n/2 observations
    • Q_3 Upper quartile = median of the largest n/2 observations
    • A measure of spread that is resident to outliers is the interquartile range IQR , given by IQR = Q_3 - Q_1

3.4 상대적위치의 측도 (Measure of relative standing)
  • P^th percentiles
  • z-score : z={x - \bar x \over s}
  • Chebyshev's inequality : Pr(|X-\mu| < k \sigma) >=1-1/k^2

Quiz 1. Email: lbg@kowon.dongseo.ac.kr
    1. The nine measurements that follow are temperature determinations at various locations beneath the surface of Lake Ontario. 4.45, 3.91, 3.86, 3.93, 3.94, 3.90, 3.80, 3.73, 3.69
    Compute :
      a. The sample mean of these data values
      b. The sample median of these data values

    2. If the price of a commodity doubles in a period of 4 years, what is the average percentage increase per year?

    3. Cities A, B, and C are equidistant from each other. A motorist travels from A to B at 30km/h, from B to C at 40km/h, and from C to A at 50km/h. Determine his average speed from the entire trip.
　

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