To find the interquartile range (IQR) of a data set, follow these steps:
- Order the data from smallest to largest.
- Find the lower quartile (Q1) , which is the value below which 25% of the data lies. This is essentially the median of the lower half of the data (not including the overall median if using the exclusive method).
- Find the upper quartile (Q3) , which is the value below which 75% of the data lies. This is the median of the upper half of the data.
- Calculate the interquartile range by subtracting the lower quartile from the upper quartile:
IQR=Q3−Q1\text{IQR}=Q_3-Q_1IQR=Q3−Q1
The IQR represents the range of the middle 50% of the data, showing the spread of the central portion of the distribution
. There are two common methods to find Q1 and Q3:
- Exclusive method: Excludes the median when splitting the data into halves for quartile calculation.
- Inclusive method: Includes the median in both halves.
The choice of method may affect the exact quartile values, especially with small data sets
. Example: Given data: 2.5, 3.1, 3.4, 3.5, 3.5, 4, 4.1
- Median (Q2) is the middle value: 3.5
- Lower half: 2.5, 3.1, 3.4 → Q1 is median of these = 3.1
- Upper half: 3.5, 4, 4.1 → Q3 is median of these = 4
- IQR = 4 - 3.1 = 0.9
This means the middle 50% of weights lie within a range of 0.9 kg
. In summary, the interquartile range is found by ordering the data, determining the first and third quartiles, then subtracting Q1 from Q3 to measure the spread of the central half of the data
