Calculate Median and Interquartile Range

Statistical Definitions:

\[ \text{Median} = \text{Middle value of ordered dataset} \] \[ \text{IQR} = Q3 - Q1 \] \[ \text{Where:} \] \[ Q1 = \text{First quartile (25th percentile)} \] \[ Q3 = \text{Third quartile (75th percentile)} \]

Median:

Interquartile Range (IQR):

First Quartile (Q1):

Third Quartile (Q3):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Are Median and IQR?

The median is the middle value in an ordered dataset, dividing it into two equal halves. The interquartile range (IQR) measures statistical dispersion by showing the range between the first quartile (Q1, 25th percentile) and third quartile (Q3, 75th percentile).

2. How Are They Calculated?

The calculations follow these steps:

\[ \text{Median} = \begin{cases} \text{Middle value} & \text{if odd number of values} \\ \text{Average of two middle values} & \text{if even number of values} \end{cases} \] \[ \text{IQR} = Q3 - Q1 \]

Where:

Data must first be sorted in ascending order
Q1 is the median of the first half of data
Q3 is the median of the second half of data
IQR represents the middle 50% of the data

3. When to Use Median and IQR

Details: Median and IQR are robust measures of central tendency and spread that are less affected by outliers than mean and standard deviation. They are particularly useful for skewed distributions.

4. Using the Calculator

Tips: Enter numerical values separated by commas. The calculator will ignore non-numeric values and calculate median, IQR, Q1, and Q3 from the remaining data.

5. Frequently Asked Questions (FAQ)

Q1: Why use median instead of mean?
A: Median is more robust to outliers and skewed data, giving a better central value for non-normal distributions.

Q2: What does IQR tell us?
A: IQR shows where the middle 50% of values lie. A larger IQR indicates more spread in the central portion of the data.

Q3: How are quartiles calculated?
A: This calculator uses the "Tukey method" (median of each half), one of several methods for calculating quartiles.

Q4: What's the relationship between IQR and outliers?
A: Values more than 1.5×IQR below Q1 or above Q3 are often considered outliers.

Q5: When should I use standard deviation instead?
A: For normally distributed data, mean ± standard deviation may be more informative.