median() in R: Find the Middle Value of a Numeric Vector

The median() function in R returns the middle value of a sorted numeric vector. It is robust to outliers, so prefer median() over mean() for skewed data, and pass na.rm = TRUE to drop missing values.

median(x)                              # 50th percentile
median(x, na.rm = TRUE)                # ignore NA values
median(mtcars$mpg)                     # median of a data frame column
median(x[x > 0])                       # conditional median (positive only)
apply(num_df, 2, median)               # column-wise median of a data frame
aggregate(mpg ~ cyl, mtcars, median)   # group-wise median by category
quantile(x, 0.5, names = FALSE)        # equivalent via quantile()

What median() does in one sentence

median() returns the middle value of a sorted vector as a single number. For an odd-length vector, it returns the exact middle element; for an even-length vector, it returns the arithmetic mean of the two middle elements.

The function is method-dispatching, so numeric, integer, logical (where TRUE = 1), and date or POSIXct vectors all have a defined median. median(Sys.Date() + 0:9) returns the midpoint date as a Date, not a number.

Syntax

median(x, na.rm = FALSE, ...) takes a vector plus one optional argument. Unlike mean(), median() has no trim argument because the median is already robust to extreme tails by construction.

The two main arguments:

• x: numeric, logical, or date or time vector
• na.rm: if TRUE, drop NA before computing; default is FALSE

Five common patterns

1. Plain median of an odd-length vector

The function sorts the vector internally to 1, 1, 3, 4, 5 and returns the third element. You do not need to sort the input yourself.

2. Even-length vector averages the two middle values

With four sorted values, the two middle elements are 2 and 3. The function returns their arithmetic mean, 2.5. This is why a median of integers can return a decimal.

3. Ignore missing values

Without na.rm = TRUE, any NA poisons the result. With it, the function drops the NA and computes the median of the remaining four values.

4. Robustness to outliers

The single outlier of 100 pulls the mean from 5.5 to 15.4. The median stays at 6.5 because rank-based summaries do not care how large the largest value is. This is the main reason to choose median() over mean() for skewed or long-tailed data.

5. Median of a data frame column

For a single column, pass it directly. For every numeric column at once, use apply(mtcars, 2, median) or sapply(mtcars, median); there is no colMedians() in base R.

median vs mean vs quantile vs mad

Pick the summary that matches the question you are asking about the distribution. The table compares four base-R summaries that operate on the same vector.

For a single robust center, use median(). For a robust pair (center + spread), use median() with mad(). For a full distributional picture, summary() or quantile() is the better entry point.

Common pitfalls

Pitfall 1: median() returns NA when any element is NA. Always set na.rm = TRUE for real-world data. If you forget, downstream summaries silently propagate NA and break plots, tables, and joins.

Pitfall 2: median of a logical vector is 0 or 1, not a proportion. mean(c(TRUE, FALSE, FALSE)) returns 0.333, but median(c(TRUE, FALSE, FALSE)) returns 0 (the middle value after sorting). Use mean() on a logical vector when you want the share that is TRUE.

Pitfall 3: passing a character vector returns NA with a warning. R does not auto-convert strings to numbers in median(). Convert first with as.numeric(), then handle the NA values that come from parse failures.

Try it yourself

Related base R summary functions

After mastering median(), look at:

• mean(): arithmetic average, paired comparison with median for skewness diagnostics
• quantile(): any percentile, including the median itself
• mad(): median absolute deviation, the robust spread for median()
• IQR(): interquartile range, another rank-based spread
• summary(): five-number summary plus mean in one call
• aggregate() and dplyr::summarise(): group-wise medians

For a full descriptive statistics tour, see the base R descriptive statistics guide. For a robust regression alternative driven by the same logic, see MASS::rlm(). The official reference for median() is the R help page.

FAQ

How do I calculate the median in R while ignoring missing values?

Pass na.rm = TRUE: median(x, na.rm = TRUE). By default, median() returns NA if any element is NA, which silently propagates into downstream summaries. Always set na.rm = TRUE when working with real-world data, or impute the missing values first using a domain-appropriate rule before summarizing.

What is the difference between median and mean in R?

mean() is the arithmetic average (sum divided by length); median() is the middle value of the sorted data. The mean is sensitive to outliers and skew; the median is not. For symmetric data the two agree; for skewed data (income, latency, counts) the median is the more honest summary of central tendency. Reporting both side by side flags the presence of skew.

How do I compute the median by group in R?

Use aggregate(x ~ group, data = df, FUN = median) in base R. For example, aggregate(mpg ~ cyl, mtcars, median) returns the median mpg for each cylinder count. The tidyverse equivalent is dplyr::summarise(median(x), .by = group). For multiple group keys, separate them with +: aggregate(mpg ~ cyl + gear, mtcars, median).

Can I compute a weighted median in base R?

Not directly. Base R has weighted.mean() but no weighted.median(). Use matrixStats::weightedMedian(x, w) or Hmisc::wtd.quantile(x, weights = w, probs = 0.5) from CRAN. A weighted median is the value at which the cumulative weight first crosses half the total weight; it is the right summary when observations contribute unequally, such as survey weights or unequal sample sizes.

Why is median(c(1, 2, 3, 4)) equal to 2.5?

For an even-length vector, no element sits exactly in the middle. R follows the standard convention of averaging the two middle values, here 2 and 3, returning 2.5. This is why a median of integers can be a decimal. If you need an integer-only result, take the lower of the two middle values with sort(x)[floor((length(x) + 1) / 2)], but this is a step-function median (quantile() type 1) and is rarely preferable to the default.