IQR Calculator — Interquartile Range

Calculate the interquartile range, lower outlier fence, and upper outlier fence from the first and third quartiles. IQR Calculator — Interquartile Range helps students, researchers, analysts, and professionals measure data spread and identify potential outliers.

Highlights

  • Calculate the interquartile range (IQR) from Q1 and Q3.
  • Measure the spread of the middle 50% of your data.
  • Identify potential outliers using lower and upper fences.
  • Use the standard Tukey method for reliable statistical analysis.
  • Get quick, clear results for research, education, and data analysis.

Table of Contents

  1. How IQR Calculator — Interquartile Range Works?
  2. Practical Use Cases
  3. Accuracy and Limitations
  4. Quick Examples
  5. Frequently Asked Questions (FAQs)
  6. Cite This Calculator

How IQR Calculator — Interquartile Range Works?

The interquartile range (IQR) measures the spread of the middle 50% of a dataset. Enter the first quartile, Q1, which represents the 25th percentile, and the third quartile, Q3, which represents the 75th percentile. The calculator then determines the range between these two quartiles.

IQR=Q3−Q1

The calculator also applies the standard Tukey outlier-fence method. The lower fence is found by subtracting 1.5 times the IQR from Q1, while the upper fence is found by adding 1.5 times the IQR to Q3.

Lower Fence=Q1−1.5×IQR
Upper Fence=Q3+1.5×IQR

For example, if Q1 is 25 and Q3 is 75, the IQR is 50, the lower fence is -50, and the upper fence is 150. Observations below the lower fence or above the upper fence may be potential outliers.


CalculationFormulaExample result
Interquartile rangeQ3 − Q175 − 25 = 50
Lower outlier fenceQ1 − 1.5 × IQR25 − 75 = -50
Upper outlier fenceQ3 + 1.5 × IQR75 + 75 = 150

Practical Use Cases

Students can use the calculator to check homework involving quartiles, summarize the spread of exam scores, and identify unusually high or low observations using the Tukey fences.

Researchers can report the middle-50-percent spread of survey, laboratory, or experimental observations and screen results for possible outliers before conducting further analysis.

Data analysts can use the IQR and outlier fences to perform quick exploratory data analysis, compare the variability of groups, and support box-plot interpretations.

Business and quality professionals can examine process measurements, transaction values, or performance indicators to flag observations that fall unusually far from the central data pattern.

Accuracy and Limitations

The calculator accurately computes the IQR as Q3 minus Q1 and the Tukey fences as Q1 − 1.5 × IQR and Q3 + 1.5 × IQR using the entered values. Q1 should normally be less than or equal to Q3; reversed or incorrectly estimated quartiles produce results that do not meaningfully describe a dataset. The calculator accepts values from -1,000,000,000 to 1,000,000,000 in increments of 0.01, but it does not calculate quartiles from raw observations or determine which individual records are outliers. Fence results identify potential outliers rather than proving that an observation is erroneous, and quartile values can differ depending on the quartile method used by the source of the data.

Quick Examples

Example #1: Typical Exam Scores

Measure the spread of the middle 50% of exam scores and identify potential outliers.

Example #2: Employee Salaries

Analyze salary dispersion and calculate potential lower and upper salary outlier thresholds.

Example #3: Daily Temperature Readings

Evaluate the central spread of daily temperatures, including a dataset with values below zero.

Frequently Asked Questions

The IQR measures the spread of the middle 50% of a dataset. A larger IQR indicates greater variability among the central observations.

Q1 is the 25th percentile, meaning 25% of observations are at or below it. Q3 is the 75th percentile, meaning 75% of observations are at or below it.

Values below the lower fence or above the upper fence may be potential outliers. These values should be reviewed in context before being excluded or treated as errors.

Yes. The IQR is relatively resistant to extreme values and is often useful for describing spread in skewed distributions.

The IQR describes the spread of the middle half of the data, while standard deviation reflects variation around the mean and can be more affected by extreme values.

Cite This Calculator