Sprint 8 Converter + Math
Mean, Median, Mode, Range Calc
Core descriptive stats.
Mean
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Median
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Mode
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Range
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How it works
Descriptive statistics summarise a dataset's central tendency and spread with a handful of numbers. Mean, median, mode, and range are the four most fundamental summary statistics, each answering a slightly different question about the data. The Mean, Median, Mode & Range Calculator computes all four (plus quartiles, IQR, and variance) from any list of numbers.
**Mean (arithmetic average)** Sum of all values divided by the count. Sensitive to outliers: one extreme value pulls the mean toward it. Used for symmetric, outlier-free distributions.
**Median (middle value)** The value at the 50th percentile when data is sorted. Robust to outliers: adding a billionaire to a group doesn't change the median income. Used for skewed distributions (income, house prices, salary surveys).
**Mode (most frequent value)** The value that appears most often. A dataset can be unimodal, bimodal, or multimodal. Used for categorical data (most popular colour, most common shoe size) and for detecting natural clusters.
**Range** Maximum minus minimum — the simplest spread measure. Sensitive to outliers; interquartile range (IQR = Q3 − Q1) is the robust alternative.
**Quartiles and IQR** Q1 (25th percentile), Q2 (median), Q3 (75th percentile). IQR = Q3 − Q1. Outliers are commonly defined as values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR (Tukey's fences).
**When mean ≠ median** Right-skewed distributions (income, property prices) have mean > median. Left-skewed distributions have mean < median. When these diverge significantly, the median is usually more representative. Financial analysts often report median household income precisely because mean income is skewed by the ultra-wealthy.
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Frequently Asked Questions
- Income distributions are right-skewed: most people earn moderate incomes, but a small number earn extremely high incomes that pull the mean up dramatically. In the US, mean household income is roughly $90,000–100,000 while median is roughly $68,000–75,000 — a ~30% gap caused by the top earners. Median better represents 'the typical person's income' because half the population earns above it and half below. Mean would misrepresent where the middle of the distribution sits when the distribution is skewed.
- Yes. A bimodal dataset has two modes (two values that appear with equal highest frequency). A multimodal dataset has three or more. Example: [2, 3, 3, 5, 7, 7, 9] → modes are 3 and 7. In statistics, multiple modes often indicate the dataset contains two or more distinct groups mixed together — the distribution is a mixture. Bimodal height data might occur if you mixed measurements from adult men and women without separating them.
- IQR = Q3 − Q1, the range of the middle 50% of data. Unlike the full range (max − min), IQR is robust to outliers because it ignores the top and bottom 25% of values. Tukey's outlier rule: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are classified as outliers. Box plots (box-and-whisker plots) display IQR as the box, with whiskers extending to non-outlier extremes. IQR is the preferred spread measure for skewed data or when outliers are expected.
- The mean is misleading for: (1) Skewed distributions — a single outlier pulls the mean away from the bulk of data. If nine people earn $30,000 and one person earns $1,000,000, the mean is $127,000, which represents no one's actual income. (2) Categorical data — the mean of shoe sizes or blood types is meaningless; use mode. (3) Ordinal data — the mean of 'satisfaction ratings' 1–5 is debatable because the intervals may not be equal. (4) Bimodal data — the mean may fall between two peaks where few actual data points exist.