When we talk about how data spreads out, we often mention things like range and interquartile range (IQR). Let’s look at some easy examples to understand these ideas better.

Example 1: Range
Imagine you have five siblings with the following ages: 10, 12, 15, 20, and 25 years old.

• To find the range, we subtract the youngest age from the oldest.
  $\text{Range} = 25 - 10 = 15$
  So, the range of ages in this group is 15 years. This number shows us how spread out the ages are.

Example 2: Interquartile Range (IQR)
Now, let’s think about some test scores: 45, 55, 60, 70, and 80.

• First, we organize the scores: 45, 55, 60, 70, 80.
• Next, we find the first quartile (Q1) and the third quartile (Q3):
  • Q1 (the score in the lower 25%) is 55.
  • Q3 (the score in the upper 25%) is 70.
• Now we can calculate the IQR:
  $\text{IQR} = Q3 - Q1 = 70 - 55 = 15$

This number, 15, helps us understand how the middle 50% of scores are spread out.

These examples show us how measures of spread, like range and IQR, help us see how data is distributed!