To find the interquartile range (IQR), you:

  1. Order the data.
  2. Find the quartiles Q1Q1Q1 and Q3Q3Q3.
  3. Subtract: IQR=Q3−Q1\text{IQR}=Q3-Q1IQR=Q3−Q1.

What IQR Means

The interquartile range measures how spread out the middle 50% of your data is.

It ignores extreme low and high values, so it’s great when your data has outliers.

Step‑by‑step: How to Find IQR

Imagine your data set is: 6, 2, 9, 4, 10, 7, 3.

1. Sort the data

  • Sorted: 2, 3, 4, 6, 7, 9, 10.

2. Find the median (Q2)

  • There are 7 values, so the 4th value is the median: Q2=6Q2=6Q2=6.

3. Split into lower and upper halves

  • Lower half (below median): 2, 3, 4
  • Upper half (above median): 7, 9, 10.

4. Find Q1 and Q3

  • Q1Q1Q1 = median of lower half = 3.
  • Q3Q3Q3 = median of upper half = 9.

5. Compute the IQR

  • IQR=Q3−Q1=9−3=6\text{IQR}=Q3-Q1=9-3=6IQR=Q3−Q1=9−3=6.

Even Number of Data Points

If you have an even number of values:

  1. Sort the data.
  2. Find the median by averaging the two middle numbers.
  3. Decide whether you:
    • Exclude the median pair when forming halves (exclusive method), or
    • Include them in the halves (inclusive method).
  1. Find Q1Q1Q1 and Q3Q3Q3 as the medians of each half.
  2. Compute Q3−Q1Q3-Q1Q3−Q1.

Both “inclusive” and “exclusive” methods are used; they can give slightly different IQRs but the idea is the same.

Why IQR Is Useful (Quick Scoop Style)

  • Helps spot outliers: values far below Q1−1.5×IQRQ1-1.5\times \text{IQR}Q1−1.5×IQR or above Q3+1.5×IQRQ3+1.5\times \text{IQR}Q3+1.5×IQR are often called outliers.
  • Describes spread: a larger IQR means the middle of your data is more spread out.
  • Works well with skewed data when the usual standard deviation is misleading.

Mini “Forum” Style Note

“Whenever I’m unsure about outliers in my dataset, I compute the IQR. If something is way beyond that range, I double‑check if it’s a real value or an error.”

Tiny TL;DR

  • Sort the data.
  • Find Q1Q1Q1 (25th percentile) and Q3Q3Q3 (75th percentile).
  • IQR = Q3−Q1Q3-Q1Q3−Q1.

Information gathered from public forums or data available on the internet and portrayed here.