Calculate the first quartile (Q1, 25th percentile) with three methods: inclusive, exclusive, and interpolated. Compare methods, view percentile table, and sorted data.
The first quartile (Q1) calculator finds the 25th percentile of your dataset, the value below which one quarter of the observations fall. Q1 is a key boundary in the five-number summary, box plots, and quartile-based spread measures.
This tool computes Q1 with three standard methods: inclusive, exclusive, and interpolated. It also shows the result on a visual number line, compares the methods, and highlights the sorted values at or below Q1.
Choose the method that matches your textbook or software, enter your data, and use the comparison to see how the lower quarter changes when the list is short or uneven.
Use this calculator when you need the lower quartile for a box plot, an outlier check, or a percentile report. It is also useful when you want to compare the effect of different quartile conventions on a small list of values.
The method comparison and highlighted sorted data make it easier to explain Q1 to students or colleagues who are new to quartiles.
Inclusive Q1: median of the lower half (including the median for odd n). Exclusive Q1: median of the lower half (excluding the median). Interpolated Q1: at rank 0.25 × (n−1), with linear interpolation between adjacent values.
Result: Q1 = 73 (inclusive)
Sorted: 68,70,72,74,76,81,84,85,88,90,92,95. Lower half: 68,70,72,74,76,81. Median of lower half = (72+74)/2 = 73. This is Q1 — 25% of the 12 exam scores are below 73.
Q1 separates the lowest 25% of the data from the rest of the distribution. In a box plot, it marks the left edge of the box and helps define the interquartile range.
Inclusive, exclusive, and interpolated methods can give slightly different Q1 values because they treat the middle of the ordered list differently. That matters most when the dataset is small.
Q1 is a useful benchmark for screening low values and describing the bottom end of a distribution. It gives a more resistant summary than the mean when a few extreme values would otherwise distort the result.
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Q1 (the first quartile, or 25th percentile) is the value below which 25% of your data falls. It divides the lower quarter from the remaining 75%. In a box plot, Q1 is the left edge of the box.
There is no single definition of quartiles. The inclusive method includes the median in both halves. The exclusive method excludes it. The interpolated method treats quartile positions as continuous. Different textbooks, software, and standards use different methods. For large datasets, they converge.
Excel QUARTILE.INC and PERCENTILE.INC use the interpolated method (linear interpolation at rank p × (n−1)). Excel QUARTILE.EXC uses a slightly different interpolation. Google Sheets follows the same approach as Excel.
In the Tukey (box plot) method, any value below Q1 − 1.5 × IQR is a mild outlier, and below Q1 − 3 × IQR is an extreme outlier. This provides a robust, non-parametric way to identify unusually low values.
They're the same concept. Q1 = P₂₅ = 25th percentile. The quartile notation (Q1, Q2, Q3) is common in descriptive statistics and box plots. The percentile notation (P₂₅) is common in standardized testing and growth charts.
You need at least 4 values to compute Q1 (enough for two values in each half). However, Q1 becomes more stable and meaningful with 20+ data points. With very small samples, Q1 may not be representative.