Statistics 통계

  • The science of collecting, analyzing, interpreting, and presenting data.
  • 데이터를 수집, 분석, 해석, 그리고 표현하는 학문입니다.

Measures of Central Tendency and Spread

  1. Mean 평균
    • The sum of all data values divided by the number of values.
    • 데이터 값의 합을 데이터 개수로 나눈 값입니다.
  2. Median 중앙값
    • The middle value of a data set when arranged in order.
    • 데이터를 크기 순으로 배열했을 때 중간에 위치한 값입니다.
  3. Mode 최빈값
    • The most frequently occurring value in a data set.
    • 데이터에서 가장 자주 나타나는 값입니다.
  4. Range 범위
    • The difference between the largest and smallest values in a data set.
    • 데이터 집합에서 가장 큰 값과 가장 작은 값의 차이입니다.
  5. Variance 분산
    • A measure of how far each value in a data set is from the mean.
    • 데이터 집합의 값들이 평균으로부터 얼마나 떨어져 있는지를 나타내는 지표입니다.
  6. Standard Deviation 표준편차
    • The square root of the variance; it measures the dispersion of a data set.
    • 분산의 제곱근으로, 데이터 집합의 흩어짐 정도를 측정합니다.

Question: 문제:
The following data shows the time students in Rick's class spent watching TV over the weekend. If the average viewing time is hours, what is the sum of the median and the mode?
다음은 지효네 반 학생 명이 주말동안 TV를 시청한 시간을 조사하여 나타낸 자료이다. TV를 시청한 시간의 평균이 시간일 때, 중앙값과 최빈값의 합을 구하시오.
Explanation: 해설:
Since the average is hours, Arranging the data in ascending order: The sum of the median and the mode is: 평균이 시간이므로 오름차순으로 정리하면, 중앙값 최빈값
Question: 문제: The following data shows the time 10 students in Rick's class spent watching TV over the weekend. If the average viewing time is 8.3 hours, what is the sum of the median and the mode? 'data:image/png;base64,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' 다음은 지효네 반 학생 10명이 주말동안 TV를 시청한 시간을 조사하여 나타낸 자료이다. TV를 시청한 시간의 평균이 8.3시간일 때, 중앙값과 최빈값의 합을 구하시오. 'data:image/png;base64,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' Explanation: 해설: Since the average is 8.3 hours,(x+73)/(10)=8.3,quad x=10Arranging the data in ascending order:[5,6,7,7,8,9,10,10,10,11]The sum of the median and the mode is:(8+9)/(2)+10=8.5+10=18.5 평균이 8.3시간이므로 (x+73)/(10)=8.3,quad x=10오름차순으로 정리하면, [5,6,7,7,8,9,10,10,10,11]중앙값 + 최빈값 =(8+9)/(2)+10=8.5+10=18.5

Data Analysis

  1. Confidence Interval 신뢰 구간
    • A range of values within which a population parameter is expected to lie with a certain level of confidence.
    • 특정 신뢰 수준에서 모집단 모수가 속할 것으로 예상되는 값의 범위입니다.
  2. Confidence Level 신뢰 수준
    • The probability that the confidence interval contains the true population parameter.
    • 신뢰 구간이 실제 모집단 모수를 포함할 확률입니다.
  3. Population 모집단
    • The entire group of individuals or objects being studied.
    • 연구의 대상이 되는 모든 개인이나 객체의 전체 집합입니다.
  4. Sample 표본
    • A subset of the population used to represent the whole.
    • 모집단을 대표하기 위해 선택된 부분 집합입니다.
  5. Standard Error 표준 오차
    • The standard deviation of the sampling distribution of a statistic.
    • 통계량의 표본 분포의 표준편차입니다.

Question: 문제:
A population follows a normal distribution with a variance of . A random sample of size is taken to estimate the population mean with a confidence interval given by . Find the minimum value of such that . (Given: ) 분산이 인 정규분포를 따르는 모집단에서 크기가 인 표본을 임의추출하여 모평균 을 신뢰도 로 추정한 신뢰구간이 이다. 이때 를 만족시키는 의 최솟값을 구하시오. (단,
Explanation: 해설:
Question: 문제: A population follows a normal distribution with a variance of 16. A random sample of size n is taken to estimate the population mean m with a 99% confidence interval given by a <= m <= b. Find the minimum value of n such that b-a <= 5. (Given: "P"(|Z| <= 2.58)=0.99) 분산이 16인 정규분포를 따르는 모집단에서 크기가 n인 표본을 임의추출하여 모평균 m을 신뢰도 99%로 추정한 신뢰구간이 a <= m <= b이다. 이때 b-a <= 5를 만족시키는 n의 최솟값을 구하시오. (단, "P"(|Z| <= 2.58)=0.99) Explanation: 해설: {:[2xx2.58 xx(4)/(sqrtn) <= 5],[sqrtn <= 4.13 cdots],[n <= 17.0404],[n=18]:} {:[2xx2.58 xx(4)/(sqrtn) <= 5],[sqrtn <= 4.13 cdots],[n <= 17.0404],[n=18]:}