Averages
The 11 salaries in an OpenStax example have a mean of about $58,682 and a median of $54,000, and one salary of $120,000 makes most of the difference. Drag points on a dot plot and watch the mean, median, mode, spread and outlier fences move with them.
Before you start
No statistics background is needed. Adding a list and dividing is enough for the mean, and sorting numbers into order is all the median asks. Some examples use large dollar amounts and decimals, so Decimals and percent helps if those still slow you down.
When you finish
You will be able to find the mean, median and mode of a data set, explain why deviations from the mean add to zero, and decide when one $5,500,000 house makes the median the better summary. You can compute a range and an interquartile range, build the 1.5 × IQR fences, and mark scores such as 45 and 25.5 as outliers.
- 1The mean as a balance pointFive quiz scores of 6, 8, 9, 7 and 10 add to 40, so their mean is 40 ÷ 5 = 8.
- 2Median and modeOf 11 salaries in an OpenStax example, the 6th in order is $54,000: five are below it and five above, so it is the median.
- 3Choosing the right averageIn OpenStax's 13 home prices, one $5,500,000 house lifts the mean to about $865,015, while the median stays at $488,800.
- 4Measuring spreadOpenStax's day class has an interquartile range of 26.5 points, while the evening class has only 11.
- 5Outliers and the 1.5 × IQR ruleIn OpenStax's evening class, the 1.5 × IQR rule marks the scores 45 and 25.5 as outliers because both are below 61.5.
Sources for this course (7)
- Curriculum: 교육부 고시 제2022-33호 [별책 8] 수학과 교육과정 (ncic.re.kr/inv/org/download.do?year=2022&seq=10003559&orgType=ogi4, PDF read 2026-10-19: 초등학교 5~6학년군 [6수04-01] 평균의 의미, 고려 사항 「평균을 구하는 방법뿐만 아니라 그 의미를 직관적으로 파악하게 한다」; 중학교 1~3학년군 [9수04-01] 중앙값·최빈값과 대푯값 고르기, [9수04-07] 분산과 표준편차, [9수04-08] 상자그림으로 분포 비교, 용어 변량·대푯값·중앙값·최빈값·도수분포표·산포도·편차·분산·표준편차·사분위수·상자그림; 고등학교 확률과 통계 용어 표본평균·모평균·표본분산·표본표준편차와 기호 X̄, S², S, N(m, σ²); 실용 통계 [12실통02-04] 대푯값과 산포도 고르기)
- Middle-school variance as the mean of the squared deviations: EBS Math 중3 「분산과 표준편차」 (www.ebsmath.co.kr/resource/rscView?cate=123500&cate2=123510&cate3=123511&rscTpDscd=RTP10&grdCd=MGRD03&sno=24525&type=S, read 2026-10-19)
- Textbook: OpenStax, Introductory Statistics 2e by Barbara Illowsky and Susan Dean, 2.3 measures of location, quartiles as medians of the lower and upper halves, IQR, 1.5 × IQR outlier rule, 13 real estate prices, 11 salaries, day and evening class test scores (openstax.org/books/introductory-statistics-2e/pages/2-3-measures-of-the-location-of-the-data)
- 2.5 measures of the center (.../pages/2-5-measures-of-the-center-of-the-data)
- 2.6 skewness and the mean, median and mode, the three ten- and sixteen-value data sets (.../pages/2-6-skewness-and-the-mean-median-and-mode)
- 2.7 measures of the spread, sample standard deviation with n − 1 (.../pages/2-7-measures-of-the-spread-of-the-data)
- Trimmed mean only: Federal Reserve Bank of Dallas, Trimmed Mean PCE inflation rate (dallasfed.org/research/pce and /research/pce/descr)
Checked: 2026-10-17