Measuring how data spreads out is really important when studying math in Year 8. Many times, we look at the average, or mean, of a group of numbers. But just knowing the average isn’t enough to understand everything. That’s where measuring spread, like range and interquartile range (IQR), comes in handy.

Why is Measuring Spread Important?

1. Understanding Differences:

   • The spread shows us how much values change from each other. If the spread is small, it means the numbers are close together. If it’s large, the numbers are more varied. For example, look at the test scores for two classes.
   • Class A has scores of 78, 79, 80, 81, and 82.
   • Class B has scores of 60, 75, 80, 85, and 90.
   • Even if both classes have the same average score, Class B has a much bigger spread and shows more differences in scores.

2. Calculating Range:

   • The range is one of the easiest ways to measure spread. You find the range by taking the highest score and subtracting the lowest score from it. For Class B, the range would be $90 - 60 = 30$. This shows that scores in Class B are more spread out.

3. Using Interquartile Range (IQR):

   • The IQR helps us see the range of the middle 50% of scores. It isn’t affected much by extreme values, which means it gives a better picture when there are outliers. To find the IQR, subtract the first quartile (Q1) from the third quartile (Q3). For example, if Q1 is 75 and Q3 is 85, then the IQR is $85 - 75 = 10$. This is especially useful when comparing groups of data that have some extreme values.

In short, measuring spread is super important for understanding data better. It helps us see more than just the average and tells a fuller story about the numbers.