Quartile Calculator

Sort the data from smallest to largest. Q2 (median) is the middle value. Q1 is the median of the lower half. Q3 is the median of the upper half. For even datasets, average the two middle values. Use the Quartile Calculator above for instant step-by-step results.

IQR = Q3 − Q1. It measures the spread of the middle 50% of your data, making it resistant to outliers. The IQR is used to identify outliers (values more than 1.5 × IQR below Q1 or above Q3) and to draw box-and-whisker plots.

After finding Q2 (median), split the dataset into lower and upper halves. For odd-count datasets, exclude the median from both halves. Q1 is the median of the lower half; Q3 is the median of the upper half. For even-count halves, average the two middle values.

Calculate the fences: Lower = Q1 − (1.5 × IQR), Upper = Q3 + (1.5 × IQR). Any data point below the lower fence or above the upper fence is considered a mild outlier. Points beyond Q1 − 3×IQR or Q3 + 3×IQR are extreme outliers.

A box plot displays the five-number summary: minimum, Q1, Q2 (median), Q3, and maximum. The box spans Q1 to Q3 (IQR). Whiskers extend to the farthest non-outlier values. Outliers are plotted as individual dots beyond the whiskers.

Percentiles divide data into 100 equal parts; quartiles divide into 4. Q1 = 25th percentile, Q2 = 50th percentile (median), Q3 = 75th percentile. Quartiles are a subset of percentiles used for quick descriptive statistics and outlier detection.

You need at least 4 data points for meaningful quartiles (one per quartile). For reliable statistical analysis, use 10+ data points. With very small datasets, quartiles may not represent the population well and should be interpreted cautiously.

Q3 + 1.5 × IQR is the upper Tukey fence. Any data point above this value is considered an outlier. For example, if Q3 = 80 and IQR = 20, the upper fence = 80 + 30 = 110. Values above 110 are outliers in that dataset.