IQR and Five-Number Summary Calculator
IQR and Five-Number Summary is evaluated from Sample Size n, Minimum value and First Quartile Q1. The calculation reports IQR, Lower Outlier Fence and Upper Outlier Fence.
Results
About the IQR and Five-Number Summary Calculator
The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.
Formula basis:
IQR = middle 50% spread. Resistant to outliers unlike range. Tukey's 1.5 x IQR rule: values more than 1.5 IQRs below Q1 or above Q3 flagged as outliers. Skewness: if Q3 - Median > Median - Q1, upper tail is longer (right-skewed).
Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.
Formula & How It Works
The calculation applies the following relations exactly as recorded in the metadata: IQR = middle 50% spread. Resistant to outliers unlike range. Tukey's 1.5 x IQR rule: values more than 1.5 IQRs below Q1 or above Q3 flagged as outliers. Skewness: if Q3 - Median > Median - Q1, upper tail is longer (right-skewed). Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.
Worked Examples
Example 1: US household income data summary: n=1000, min=$18k, Q1=$45k, median=$70k, Q3=$105k, max=$350k
Inputs
With Sample Size n = 1,000, Minimum value = 18,000, First Quartile Q1 = 45,000 and Median = 70,000 as the stated inputs, the result is IQR = 60,000, Lower Outlier Fence = -45,000 and Upper Outlier Fence = 195,000. Each value corresponds to the declared output fields.
Example 2: Student test scores: n=30, min=45, Q1=68, median=75, Q3=85, max=99
Inputs
With Sample Size n = 30, Minimum value = 45, First Quartile Q1 = 68 and Median = 75 as the stated inputs, the result is IQR = 17, Lower Outlier Fence = 42.5 and Upper Outlier Fence = 110.5. Each value corresponds to the declared output fields.
Example 3: Housing prices in a zip code: n=50, min=$180k, Q1=$285k, median=$340k, Q3=$425k, max=$1.2M
Inputs
With Sample Size n = 50, Minimum value = 180,000, First Quartile Q1 = 285,000 and Median = 340,000 as the stated inputs, the result is IQR = 140,000, Lower Outlier Fence = 75,000 and Upper Outlier Fence = 635,000. Each value corresponds to the declared output fields.
Example 4: Reaction times (ms) in psychology experiment: n=20, min=210ms, Q1=245ms, median=260ms, Q3=285ms, max=420ms
Inputs
With Sample Size n = 20, Minimum value = 210, First Quartile Q1 = 245 and Median = 260 as the stated inputs, the result is IQR = 40, Lower Outlier Fence = 185 and Upper Outlier Fence = 345. Each value corresponds to the declared output fields.
Common Use Cases
- Calculate IQR and five-number summary for a dataset
- Identify outliers using the 1.5×IQR fence rule
- Prepare data summary statistics for box plots