Biostatistics #3 (Describing Data: Central Tendency 집중경향성)

We need a method to summarize each group as a whole so that we can objectively describe how much difference exists between the two groups. 

 

Central Tendency (집중 경향성)

: 모집단이나 표본으로부터 얻어진 자료가 어떤 특정 값을 중심으로 분포를 형성하는 경향 (= 점수값이 어떤 식으로 분포되어 있는지)

: a statistical measure to determine a single value that defines the center of a distribution.

==> The goal of central tendency is to find the single value that is most typical or representative of the entire group.   

 

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Unfortunately, there is no single, standard procedure for determining central tendency. No single measure will always produce a central representative value in every situation.

하지만, 어떤 하나의 척도도 모든 상황에서 항상 중심 대표 값을 산출하지는 않는다.

 

예를 들어,

 

a) symmetrical, center = 5 ==> it is easy to find the center. 

b) asymmetrical, midpoint = 5, but highest frequency  = 8, average would be higher than 5. 

c) symmetrical, midpoint = 5, but two distinct piles of scores 

 

The solution is three different methods for measuring central tendency: Mean, Median, and Mode. 

 

 

 

 

Measures of Central Tendency 

 

1. Mean (평균, arithmetic mean) : 개체의 모든 점수값을 더한 후, 그 개체의 수로 나눈 값.

: the sum of the values divided by the number of values

- calculated by adding all the data and dividing by their N. 

- mean for a population (μ) / mean for a sample (x̄)

• Characteristics of the Mean
  • changing the value of any score will change the mean
  • adding or removing a score will usually (but not always) change the mean. The exception to this is when the new score added (or the score removed) is exactly equal to the mean.
  • adding or subtracting a constant value from each score will add or subtract the same constant from the mean
  • multiplying or dividing each of the scores will produce a mean that is multiplied or divided by the same factor. 

 

2. Median (중앙값) : 어떤 집단의 점수값을 적은 것으로부터 큰 것으로 차례로 나열한 후, 그 나열된 점수 중 가운데에 해당하는 값. 

: the score that divides a distribution in half so that 50% of the individuals in distribution have scores at or below the median. 

- the goal of the median is to determine the midpoint of the distribution 

- no special differentiation between sample median and population median. 

- appropriate for skewed/open-ended distributions, and distributions with undetermined scores

• Put the scores in ascending order and find the middle value
  • If N is odd, the median is the middle score 
  • If N is even, the median is the mean of the middle two scores 

3. Mode (최빈값): 어떤 집단의 점수값 중 가장 많은 빈도의 값

: the score or category that has the greatest frequency.

- appropriate for nominal data

• It is possible to have more than one mode in a given distribution. (Note: it is not possible to have more than one mean or median)
  • A distribution with two modes is called bimodal. One with multiple modes is called multimodal.
  • If two modes have unequal frequencies, one is called the major mode and the other is called the minor mode. 

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Central Tendency & the Shape of the Distribution

분포의 모양에 따라 평균, 중앙값, 최빈값이 다른 값을 가지기도 한다.

 

 

 

출처: 네이버 지식백과, Youtube > Academic Lesson