interquartile and outliers

사분범위 = Q3 - Q1
사분범위 = (상한사분위수) - (하한사분위수)

• 하한
  • n / 4 = ?
  • 정수이면? 그 위치값과 다음 위치 값의 사이값
  • 정수가 아니면? 올림을 한 위치의 값
• 상한
  • 3n / 4 = ?
  • 정수이면? 그 위치 값과 그 다음에 위치 값의 사이값
  • 정수가 아니면? 올림을 한 위치 값

> k <- c(1:8)
> k
[1] 1 2 3 4 5 6 7 8
> quantile(k)
  0%  25%  50%  75% 100% 
1.00 2.75 4.50 6.25 8.00 
> 

그러나, 위의 방법으로는
lower quartile: 2.5
upper quartile: 6.5

• Use the median to divide the ordered data set into two halves.
• If there is an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
• If there is an even number of data points in the original ordered data set, split this data set exactly in half.
• The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.
• This rule is employed by the TI-83 calculator boxplot and “1-Var Stats” functions.

• Use the median to divide the ordered data set into two halves.
• If there are an odd number of data points in the original ordered data set, include the median (the central value in the ordered list) in both halves.
• If there are an even number of data points in the original ordered data set, split this data set exactly in half.
• The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.
• The values found by this method are also known as “Tukey's hinges.”

Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

in r

> k <- c(1:8)
> k
[1] 1 2 3 4 5 6 7 8
> quantile(k)
  0%  25%  50%  75% 100% 
1.00 2.75 4.50 6.25 8.00 
> 

in r

> duration = faithful$eruptions     # the eruption duration
> quantile(duration)                # apply the quantile function 
    0%    25%    50%    75%   100% 
1.6000 2.1627 4.0000 4.4543 5.1000

quantile, not qurtile