Bright Range, Quartiles & IQR Calculator

Range, Quartiles & IQR Calculator

Calculate statistical measures for your dataset with our vibrant and interactive tool

Input Data

Individual Values

Values with Frequency

Definitions and Formulas

Range

The range is the difference between the largest and smallest values in a dataset.

Range = Maximum Value – Minimum Value

It gives a quick sense of the spread of the data but is sensitive to outliers.

Quartiles

Quartiles divide a ranked dataset into four equal parts:

  • Q1 (First Quartile): The value below which 25% of the data falls
  • Q2 (Second Quartile/Median): The value below which 50% of the data falls
  • Q3 (Third Quartile): The value below which 75% of the data falls

Interquartile Range (IQR)

The IQR measures the statistical dispersion of the middle 50% of data values.

IQR = Q3 – Q1

The IQR is used to identify outliers and understand the spread of the central portion of a dataset. Values that fall below Q1 – 1.5×IQR or above Q3 + 1.5×IQR are considered outliers.

Calculation Methodology

This calculator uses the following method to calculate quartiles:

  1. Sort the data in ascending order
  2. Find the median (Q2) which divides the data into two halves
  3. Find the median of the lower half (Q1)
  4. Find the median of the upper half (Q3)

For datasets with an odd number of observations, the median is excluded from both halves when calculating Q1 and Q3.

Applications of Range and IQR

Range is useful for:

  • Quick assessment of data spread
  • Understanding the scope of variation in the data
  • Identifying the minimum and maximum values

Interquartile Range (IQR) is useful for:

  • Identifying outliers in the data
  • Understanding the spread of the middle 50% of data
  • Comparing variability between different datasets
  • Creating box plots for data visualization