Chapter 1. Introduction

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Chapter_01_Korean.pdf

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Chapter_01_Chinese.pdf

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1.1 기본 정의 및 개념

• A population(모집단) is any specific collection of objects of interest. A sample is any subset or subcollection of the population, including the case that the sample consists of the whole population, in which case it is termed a census.

• A measurement(측정치) is a number or attribute computed for each member of a population or of a sample. The measurements of sample elements are collectively called the sample data.

• A parameter(모수) is a number that summarizes some aspect of the population as a whole. A statistic is a number computed from the sample data.

• Statistics is a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data.

• Descriptive statistics is the branch of statistics that involves organizing, displaying, and describing data.

• Inferential statistics is the branch of statistics that involves drawing conclusions about a population based on information contained in a sample taken from that population.

• Qualitative data are measurements for which there is no natural numerical scale, but which consist of attributes, labels, or other nonnumerical characteristics.

• Quantitative data are numerical measurements that arise from a natural numerical scale.

Grand Picture of Statistics

1.2 Overview

• The sample average is an example of what is called a random variable: a number that varies from trial to trial of an experiment (in this case, from sample to sample), and does so in a way that cannot be predicted precisely.

• A different samples have different levels of reliability.

• Single estimation

• The confidence interval: from the data we will construct an interval of values so that the process has a certain chance, say a 95% chance, of generating an interval that contains the actual population average.

• probability

• Sampling

• ...

1.3 Presentation of Data

EXAMPLE 1. 임의로 선택된 21명 학생들의 나이 데이터이다. 이들 데이터에 대한 도수 분포표를 작성하라.

18 18 19 19 19 18 22 20 18 18 17 19 18 24 18 20 18 21 20 17 19

R Source

age <- c(18, 18, 19, 19, 19, 18, 22, 20, 18, 18, 17, 19, 18, 24, 18, 20, 18, 21, 20, 17, 19)

# 1. Frequency Table
y <- table(age) ; y

# 2. Relative Frequency Table
prop.table(y)

# 3. Frequency Diagram
plot(y)

# 4. Relative Frequency Diagram
plot(prop.table(y))

Frequency Table

> # 1. Frequency Table
> y <- table(age); y
## age
## 17 18 19 20 21 22 24 
##  2  8  5  3  1  1  1 
>
> # 2. Relative Frequency Table
> prop.table(y)
## age
##         17         18         19         20         21         22         24 
## 0.09523810 0.38095238 0.23809524 0.14285714 0.04761905 0.04761905 0.04761905 
> 

Plot

• Frequency Diagram

• Relative Frequency Diagram

위의 데이터 세트에 대한 도수 분포표(frequency table)가 작성되었다. 이 표에는 x 의 유일값이 첫 번째 행에 나열이 되고, 두번째 행에는 데이터 세트에 나타나는 x 값의 빈도(frequency) f 값이 출력된다.