The interquartile range (IQR) is an important way to look at how spread out data is.

It helps us see the range of the middle 50% of values in a set of numbers.

What is IQR?

• How to Calculate It: To find the IQR, you use this simple formula:
  $\text{IQR} = Q_3 - Q_1$
  Here, $Q_1$ is the first quartile (the value at the 25th percentile), and $Q_3$ is the third quartile (the value at the 75th percentile).

• Example in Real Life:
  Let’s say we have test scores from a class:

  • $Q_1$ = 70 (25% of students scored this low or lower)
  • $Q_3$ = 85 (75% of students scored this low or lower)
  • So, the IQR is $85 - 70 = 15$.

Why IQR Matters:

• Less Variation:
  If the IQR is small, it means the scores are close to the middle score (or median). This shows that the students performed similarly.

• Finding Outliers:
  The IQR also helps us find outliers, which are scores that are much higher or lower than the rest. Any score below $Q_1 - 1.5 \times \text{IQR}$ or above $Q_3 + 1.5 \times \text{IQR}$ would be considered an outlier.

Understanding the IQR is very important in statistics. It gives us a clear picture of how data is spread out and how consistent it is.