When students in Year 9 look at survey results, it's really important for them to understand how spread out the answers are. This is called measures of dispersion. These measures help us go beyond just looking at the average answers.

What Are Measures of Dispersion?

1. Range: This is the easiest way to see how spread out the data is. You find it by subtracting the smallest value from the biggest value. For example, if students say they spend between 1 to 5 hours on homework, the range would be $5 - 1 = 4$ hours. This means there’s a variety in how much time students are putting into homework.

2. Variance: This tells us how much the data points differ from the average, but in a little more complicated way. To figure it out, we take the average of the squared differences from the average answer. It’s a formula that looks like this: $\text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n}$ Here, $x_i$ are the different answers, and $\bar{x}$ is the average. Variance helps show us how far the answers are from the average.

3. Standard Deviation: This is just the square root of the variance. It helps us see the spread in the same units as the data, making it easier to understand. It shows how much, on average, each response varies from the average answer.

Why Are They Important?

Looking at these measures helps students make smart choices based on survey results. They can see patterns and understand differences in opinions or experiences.

For example, if a survey asks about favorite subjects and most students choose Mathematics with a low standard deviation, it means that many students really like this subject. Knowing how spread out the answers are helps teachers make better decisions about how to teach and what subjects to focus on in class.