In everyday life, it’s really important to understand how data can spread out. This is called measures of dispersion, and the main types are range, variance, and standard deviation. Let’s break these down with some examples.

1. Range: Imagine a classroom with 30 students who took a test. Their scores go from 50 to 95. To find the range, you subtract the lowest score from the highest:

   • Range = Maximum - Minimum
   • Range = 95 - 50 = 45 This shows how much the scores can differ.

2. Variance: Now let’s look at how students study each week. If some study for 10, 12, 10, 14, and 16 hours, we first find the average (mean):

   • Mean = 12 hours Variance helps us understand how much the study hours are different from the average. To find it, we look at how far each number is from the mean and then average those differences:
   • Variance = ((10-12)² + (12-12)² + (10-12)² + (14-12)² + (16-12)²) / 5 = 4 This tells us the variation in study hours.

3. Standard Deviation: This is a bit easier to understand. The standard deviation (SD) is just the square root of the variance. It tells us the average distance of each data point from the average:

   • SD = √4 = 2 A smaller SD means the study hours are closer to the average.

Knowing these measures helps us understand how consistent or varied things can be. This applies to school grades, sports scores, and so much more!