What Is a Median Calculator?

A median calculator finds the middle value of a dataset after sorting it in ascending order. Pre-filled with the sequence {4, 8, 15, 16, 23, 42} (the famous Lost numbers), the median is 15.5 — the average of the two middle values in this even-count dataset. The calculator also computes mean, mode, range, standard deviation, and variance for complete descriptive statistics.

How to Calculate the Median

Step 1: Collect all values. Step 2: Sort in ascending order. Step 3: If n is odd — median = value at position (n+1)/2. If n is even — median = (value at n/2 + value at n/2+1) / 2. For {4, 8, 15, 16, 23, 42}: n=6 (even), median = (15+16)/2 = 15.5.

Median vs Mean vs Mode

The three measures of central tendency: Mean: arithmetic average — sensitive to outliers. Median: middle value — robust to outliers. Mode: most frequent — useful for categorical data. For income data: the mean ($59,000) is pulled up by high earners, while the median ($35,000) better represents the typical worker. This is why income statistics typically report median household income.

When Does Median Beat Mean?

Skewed distributions: right-skewed (housing prices, wealth) — median better. Left-skewed (age at retirement) — median better. Outliers present: a single extreme value shifts the mean drastically but barely affects the median. Ordinal data: rankings, Likert scales — median is more appropriate. Real estate: "median home price" is standard because a few luxury homes would inflate the mean.

Weighted Median

A weighted median assigns importance to values. Each value has a weight, and the weighted median is the value where accumulated weight reaches 50%. Used in: portfolio analysis (weighted by asset value), spatial median calculations, image processing (noise reduction). The standard median is a special case where all weights are equal.

Median Absolute Deviation (MAD)

MAD = median(|xᵢ − median|) — a robust measure of spread analogous to standard deviation but using medians instead of means. MAD is highly resistant to outliers: one extreme value can completely distort the standard deviation but barely affects MAD. Used in: outlier detection, robust statistics, financial risk analysis. MAD × 1.4826 estimates the standard deviation for normal distributions.