First Quartile Calculator
Find the lower quartile (Q1) of 2 – 30 numeric observations using the median of the lower half of the ordered data.
Data
Separate values with commas, semicolons, spaces, or line breaks. Use a period for decimals. Scientific notation and unit symbols are not accepted.
Method: sort ascending, exclude the overall median when the observation count is odd, then take the median of the lower half.
Result
First quartile (Q1)
19.5
Observation count
9
Dataset median
28
Lower-half count
4
Q1 is the median of 12, 18, 21, 24.
Sorted data
The table shows the ordered observations and which values participate in the lower-half median.
| Rank | Value | Role |
|---|---|---|
| 1 | 12 | Lower half |
| 2 | 18 | Lower half |
| 3 | 21 | Lower half |
| 4 | 24 | Lower half |
| 5 | 28 | Overall median |
| 6 | 31 | Upper half |
| 7 | 35 | Upper half |
| 8 | 42 | Upper half |
| 9 | 47 | Upper half |
For an odd-sized data set, the overall median is not included in either half. For an even-sized data set, the lower half contains exactly n ÷ 2 observations.
How to use this first quartile calculator
What this calculator does
This calculator finds the first quartile, also called the lower quartile or Q1, for a small numeric data set. Q1 is a measure of position: it marks the center of the lower half of ordered observations and is commonly described as the 25th percentile. The calculator is designed for descriptive statistics on 2 to 30 observed numbers. It sorts the values, identifies the lower half, and takes that half's median. It does not infer a population distribution, estimate confidence intervals, or decide whether a value is an outlier. For a broader explanation of quartiles as special percentiles, see the OpenStax guide to measures of location.
When to use it
- Summarize the lower portion of a set of test scores, response times, prices, measurements, or other numeric observations.
- Check a hand calculation before building a five-number summary or box plot.
- Compare the lower quartile of two small samples after calculating each sample separately.
- Inspect which ordered values actually determine Q1 when the sample size is odd or even.
How to calculate
The calculator opens with a complete demonstration data set, so the first result and the example Excel workbook are available immediately. To use your own sample:
- Replace the demonstration numbers in Values (2 – 30 numbers) with your observations. Separate entries with commas, semicolons, spaces, or line breaks.
- Read First quartile (Q1) in the results panel. The supporting cards show Observation count, Dataset median, and Lower-half count.
- Review the Sorted data table to see each Rank, its Value, and its Role in the split.
- Select Download Excel to export the current valid data, calculated outputs, and sorted rows to an XLSX workbook.
- Select Reset to clear the demonstration and all calculated content. After Reset, Excel export is disabled until a complete valid data set is entered again.
Input guide
Values (2 – 30 numbers) is the only data input and is required. Enter ordinary finite numbers without units. A value may be positive, zero, or negative. Decimals use a period, such as 12.5; a comma is treated as a separator between observations, not as a decimal comma. Scientific notation such as 1e3, currency symbols, percent signs, and mixed text are rejected so the sample cannot be silently reinterpreted. A realistic entry is 31, 12, 47, 24, 18, 35, 21, 42, 28. Changing any observation can change the ordering and therefore which values form the lower half. A common mistake is assuming the numbers must be pre-sorted; they do not, because sorting is part of the calculation.
Output guide
First quartile (Q1) is the calculator's primary result and uses the same unit as the observations. It is an exact result under this calculator's stated quartile convention, not a forecast or recommendation. Observation count is the exact number of valid values supplied. Dataset median is the midpoint of the full ordered data set and helps show where the sample is split. Lower-half count is the number of observations used to compute Q1: it equals half the sample for an even count and excludes the single overall median for an odd count. In the Sorted data table, Rank is the ascending position, Value is the numeric observation, and Role identifies whether the row belongs to the lower half, is the overall median, or belongs to the upper half. Duplicate values are retained because each observation keeps its own rank.
Worked example
The startup example contains nine observations: 31, 12, 47, 24, 18, 35, 21, 42, and 28. After sorting, the sequence is 12, 18, 21, 24, 28, 31, 35, 42, 47. Because there are nine values, 28 is the overall median and is excluded from the lower half. The lower half is therefore 12, 18, 21, 24. Its median lies between 18 and 21, so Q1 = (18 + 21) ÷ 2 = 19.5. That is why the first-open result is 19.5, with an observation count of 9, a dataset median of 28, and a lower-half count of 4. This lower-half-median definition is also described in Penn State's statistical concepts lesson on quartiles and percentiles.
How the first-quartile method works
First, the observations are ordered from smallest to largest. If the full data set has an even number of values, it is split into two equal halves. If it has an odd number, the single overall median is left out and the values below it become the lower half. Q1 is then the median of that lower half. When the lower half itself has an even number of values, its median is the arithmetic mean of its two center values; when it has an odd number, its center value is Q1 directly. This method is especially transparent for small samples because every contributing observation can be inspected in the sorted table.
Why quartile answers can differ across software
There is more than one accepted sample-quantile convention. Some statistical packages define the 25th percentile through an interpolated rank formula rather than the median-of-halves procedure used here. For some sample sizes, those methods produce the same number; for others, they do not. The NIST Engineering Statistics Handbook discussion of percentiles explicitly notes that multiple percentile-estimation methods are used in practice. When comparing results between tools, verify the quartile definition before treating a numerical difference as an error.
Interpreting Q1 responsibly
Q1 is useful because it resists the influence of very large upper-tail values better than a mean does, but it summarizes position rather than overall spread. A low Q1 means the lower portion of the sample is concentrated at lower values relative to the sample's scale; a higher Q1 shifts that lower-quarter boundary upward. Q1 by itself does not show how dispersed the middle half is. For that, Q1 is usually paired with Q3 to calculate the interquartile range, IQR = Q3 – Q1, and with the median, minimum, and maximum in a five-number summary. If the data are a sample from a larger process or population, remember that the computed Q1 describes the supplied observations under the selected convention; it is not automatically a precise population percentile.