2 Algebra
2.1 Mean, Median, Mode
Algebra에서 맨 처음 소개할 내용은 자료들의 대표값에 대한 내용입니다. 크게 세가지 평균,중간값, 최빈값입니다.
1 2 2 4 11
평균은 4
중간값은 2 최빈값은 2
만약 4가 추가가 된다면
평균은 여전히 4
중간값은 가운데 2 4의 단순평균인 3
최빈값들은 2, 4입니다.
There could be multiple modes. If the problem says “unique mode”, it means that there is only one mode
이외에도 여러 가지 평균이 있습니다.
The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.
The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of numbers.
The quadratic mean (also called the root mean square) is a type of average. It measures the absolute magnitude of a set of numbers, and is calculated by:
Squaring each number,
Finding the mean of these squares,
Taking the square root of that average.
하지만 전혀 걱정할 필요 없습니다. 위의 세 가지 이외에는 정확하게 설명이 나옵니다. 그 설명을 이해하고 문제에서 원하는 조작을 따라 갈 수 있으면 되는 것이지 기억할 필요는 없습니다.
문제를 보겠습니다.
2019 AMC 10/AMC 12 Problem 13
What is the sum of all real numbers x for which the median of the numbers 4,6,8,17, and x is equal to the mean of those five numbers?
//-5
2001 AIME I Problem 2
A finite set S of distinct real numbers has the following properties: the mean of (S union {1}) is 13 less than the mean of S, and the mean of (S union 2001) is 27 more than the mean of S. Find the mean of S. 651
2023 AMC 12A Problems/Problem 8
Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an 11 on the next quiz, her mean will increase by 1. If she scores an 11 on each of the next three quizzes, her mean will increase by 2. What is the mean of her quiz scores currently? 7
2022 AMC 10B Problems/Problem 10
Camila writes down five positive integers. The unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. What is the least possible value for the mode?11
2022 AMC 10A Problems/Problem 8
A data set consists of 6 (not distinct) positive integers: 1,7,5,2,5, and X. The average (arithmetic mean) of the 6 numbers equals a value in the data set. What is the sum of all positive values of X?36