제1 장 통계학의 이해
1.1 통계학의 의미 ······························································································· 3
1.2 통계학의 분류 ······························································································· 4
1.3 모집단과 표본 ······························································································· 7
1.4 데이터 마이닝 ····························································································· 13
4차 산업혁명 _ 13
빅데이터 _ 15
비즈니스 분석론 _ 16
인공지능 _ 19
데이터 마이닝 _ 20
▶ 연습문제 ········································································································· 22


제2 장 기술통계학Ⅰ：데이터의 정리 및 표현
2.1 데이터의 종류 ····························································································· 27
범주 데이터와 수치 데이터 _ 28
이산 데이터와 연속 데이터 _ 29
단변수 데이터와 다변수 데이터 _ 30

2.2 측정척도의 형태 ························································································· 32
명목척도 _ 32
서열척도 _ 33
구간척도 _ 34
비율척도 _ 34
2.3 도수분포표 ·································································································· 36
기본 개념 _ 36
도수분포표의 그래프 _ 37
2.4 범주 데이터의 정리 ···················································································· 37
도수분포표 _ 37
도수분포표의 그래프 _ 40
2.5 수치 데이터의 정리：이산 데이터 ····························································· 45
도수분포표 _ 45
도수분포표의 그래프 _ 46
2.6 수치 데이터의 정리：연속 데이터 ····························································· 47
도수분포표의 그래프 _ 50
2.7 EXCEL 활용 ································································································ 53
▶ 연습문제 ········································································································· 64


제3장 기술통계학Ⅱ：요약통계량
3.1 중심경향의 측정치 ······················································································ 73
산술평균 _ 74
중앙치 _ 75
최빈치 _ 76
평균, 중앙치, 최빈치의 비교 _ 77
3.2 산포의 측정치 ····························································································· 78
범위 _ 80
중간범위 _ 81
평균절대편차 _ 82
분산과 표준편차 _ 83
Chebyshev의 정리 _ 88
변동계수 _ 90
3.3 상대위치의 측정치 ······················································································ 91
백분위수 _ 92
사분위수 _ 93
Z 값 _ 94
3.4 형태의 측정치 ····························································································· 97
비대칭도 _ 97
첨도 _ 99
3.5 EXCEL 활용 ·······························································································100
▶ 연습문제 ········································································································108


제4장 확률이론
4.1 사상과 표본공간 ························································································113
4.2 집합이론 ····································································································118
집합의 개념 _ 118
집합의 종류 _ 119
4.3 확률의 정의 ·······························································································124
고전적 방법 _ 125
상대도수 방법 _ 125
주관적 방법 _ 127
4.4 확률의 공리 ·······························································································127
4.5 확률의 연산법칙 ························································································129
덧셈법칙 _ 129
조건확률 _ 132
곱셈법칙 _ 140
4.6 Bayes 정리 ································································································142
개념 _ 142
표의 이용 _ 144
4.7 EXCEL 활용 ·······························································································146
▶ 연습문제 ········································································································147


제5장 확률변수와 확률분포
5.1 확률변수 ····································································································155
5.2 확률분포 ····································································································157
이산확률분포 _ 158
연속확률분포 _ 160
5.3 확률함수 ····································································································161
확률질량함수 _ 162
확률밀도함수 _ 164
5.4 확률변수의 기대값과 분산 ·········································································167
기대값의 의미 _ 167
기대값의 특성 _ 168
분산 _ 169
5.5 결합확률분포 ·····························································································173
결합확률분포의 개념 _ 173
조건확률 _ 175
두 변수의 독립성 _ 176
5.6 공분산과 상관계수 ·····················································································177
공분산 _ 177
상관계수 _ 179
5.7 EXCEL 활용 ·······························································································180
▶ 연습문제 ········································································································184


제6장 확률분포Ⅰ：이산확률분포
6.1 베르누이 시행 ····························································································191
6.2 이항분포 ····································································································192
이항 확률질량함수의 이용 _ 193
이항확률표의 이용 _ 195
6.3 이항분포의 형태 ························································································197
6.4 이항분포의 기대값과 분산 ·········································································199
6.5 포아송분포 ·································································································202
개념 _ 202
포아송 확률질량함수의 이용 _ 203
포아송 분포표의 이용 _ 204
6.6 초기하분포 ·································································································206
개념 _ 206
초기하분포의 확률질량함수 _ 207
6.7 EXCEL 활용 ·······························································································209
▶ 연습문제 ········································································································211


제7장 확률분포Ⅱ：연속확률분포
7.1 확률밀도함수 ·····························································································217
7.2 정규분포 ····································································································219
정규분포의 사용 _ 219
정규곡선의 형태 _ 219
정규곡선의 특성 _ 220
7.3 표준정규분포 ·····························································································224
정의 _ 224
표준정규분포표의 이용 _ 230
정규분포의 응용 예 _ 238
7.4 이항분포의 정규근사 ·················································································241
7.5 지수분포 ····································································································243
개념 _ 243
지수분포의 확률 _ 245
7.6 EXCEL 활용 ·······························································································247
▶ 연습문제 ········································································································252


제8장 표본분포
8.1 표본추출 ····································································································259
표본조사의 필요성 _ 259
표본오차와 비표본오차 _ 260
8.2 표본추출 과정 ····························································································262
8.3 표본추출 방법 ····························································································263
확률 추출방법 _ 264
비확률 추출방법 _ 266
8.4 표본분포 ····································································································266
8.5 평균의 표본분포：복원추출 ······································································269
개념 _ 269
평균의 표본분포의 기대값과 분산 _ 273
평균의 표준오차 _ 275
8.6 평균의 표본분포：비복원추출 ··································································277
8.7 중심극한정리 ·····························································································281
표본크기의 영향 _ 281
모집단이 정규분포를 따를 때 _ 282
모집단이 정규분포를 따르지 않을 때 _ 284
8.8 비율의 표본분포 ························································································287
개념 _ 287
비율의 표본분포의 기대값과 표준편차 _ 289
이항분포의 정규근사 _ 292
유한 모집단에서의 표본비율의 표준편차 _ 293
8.9 EXCEL 활용 ·······························································································294
▶ 연습문제 ········································································································298


제9장 통계적 추정：한 모집단
9.1 점추정과 구간추정 ·····················································································305
9.2 추정량의 결정기준 ·····················································································306
불편성 _ 307
효율성 _ 308
일관성 _ 309
충족성 _ 310
9.3 신뢰구간 추정 ····························································································311
개념 _ 311
오차율 _ 313
9.4 모평균의 신뢰구간 ·····················································································314
모표준편차를 아는 경우 _ 314
모표준편차를 모르는 경우：소표본 _ 320
9.5 t 분포 ·········································································································320
모표준편차를 모르는 경우：대표본 _ 327
9.6 모비율의 신뢰구간 ·····················································································329
9.7 표본크기 결정 ····························································································331
모평균 추정 _ 331
모비율 추정 _ 334
9.8 모분산의 신뢰구간 ·····················································································336
χ2 분포의 특성 _ 337
모분산의 신뢰구간 _ 341
9.9 EXCEL 활용 ·······························································································344
▶ 연습문제 ········································································································348


제10장 가설검정：한 모집단
10.1 가설검정 ····································································································355
가설의 의미와 종류 _ 355
가설의 설정 _ 356
가설의 형태 _ 358
가설검정의 오류 _ 360
결정규칙 _ 362
가설검정의 순서 _ 366
10.2 모평균의 가설검정 ·····················································································367
모표준편차를 아는 경우 _ 368
모표준편차를 모르는 경우 _ 378
10.3 모비율의 가설검정 ·····················································································383
10.4 모분산의 가설검정 ·····················································································387
10.5 EXCEL 활용 ·······························································································390
▶ 연습문제 ········································································································395


제11장 통계적 추정과 가설검정：두 모집단
11.1 표본의 독립성과 종속성 ············································································403
11.2 두 표본평균 차이의 표본분포 ····································································404
11.3 두 모평균 차이에 대한 추정과 검정 ··························································406
독립표본 _ 406
대응표본 _ 414
11.4 두 모비율 차이에 대한 추정과 검정 ··························································418
11.5 두 모분산 비율에 대한 추정과 검정 ··························································423
F 분포 _ 423
두 모분산 비율의 추정 _ 427
두 모분산 비율의 검정 _ 428
11.6 EXCEL 활용 ·······························································································431
▶ 연습문제 ········································································································438


제12장 분산분석
12.1 분산분석의 의미 ························································································447
12.2 실험설계의 기본 개념 ················································································448
12.3 분산분석의 기본 원리 ················································································450
12.4 일원배치법：반복 수가 같은 경우 ····························································452
12.5 이원배치법：반복없는 경우 ······································································462
12.6 이원배치법：반복 있는 경우 ·····································································468
12.7 EXCEL 활용 ·······························································································475
▶ 연습문제 ········································································································480


제13장 회귀분석과 상관분석
13.1 회귀분석과 상관분석 ·················································································487
13.2 산포도 ········································································································488
13.3 단순선형회귀모델 ······················································································491
확정적 모델과 확률적 모델 _ 491
모집단 단순회귀모델 _ 492
표본 회귀모델 _ 494
오차항에 대한 가정 _ 496
13.4 최소자승법 ·································································································498
13.5 표본회귀선의 적합도 검정 ·········································································502
13.6 상관분석 ····································································································510
공분산 _ 510
상관계수 _ 512
13.7 표본회귀선의 유의성 검정 ·········································································515
13.8 종속변수 Y 의 추정과 예측 ········································································520
13.9 EXCEL 활용 ·······························································································526
▶ 연습문제 ········································································································534


제14장 다중회귀분석
14.1 다중회귀모델 ·····························································································541
다중선형회귀모델 _ 541
다중회귀모델의 가정 _ 543
14.2 최소자승법 ·································································································544
14.3 다중표본회귀식의 적합도 검정 ·································································546
추정치의 표준오차 _ 546
결정계수 _ 548
14.4 다중회귀모델에 대한 유의성 검정 ·····························································550
F 검정 _ 550
t 검정 _ 552
14.5 종속변수 Y 의 예측 ····················································································555
14.6 범주적 독립변수 ························································································557
▶ 연습문제 ········································································································561


제15장 χ2 검정과 비모수통계학
15.1 모수통계학과 비모수통계학 ······································································569
15.2 모집단 분포의 적합도 검정 ·······································································570
모비율의 검정 _ 571
모집단 분포의 검정 _ 575
15.3 두 변수 간의 독립성 검정 ··········································································580
15.4 EXCEL 활용 ·······························································································584
▶ 연습문제 ········································································································586

부표
A. 이항분포표 ··································································································· 592
B. e-μ의 값 ······································································································· 595
C. 포아송분포표 ······························································································· 596
D. 표준정규분포표 ···························································································· 598
E. 난수표 ··········································································································· 599
F. t 분포표 ········································································································· 600
G. χ2분포표 ······································································································ 601
H. F 분포표 ······································································································· 603
◈ 영문색인 ················································································································ 607
◈ 국문색인 ················································································································ 612