Understanding range, variance, and standard deviation is important for Year 1 students who are starting to learn about statistics. These terms help us see how data points are spread out around the average. Let’s break down these concepts with simple steps!

1. Range

The range is the easiest way to see how spread out the values are. To find the range, follow these steps:

• Step 1: Look for the highest and lowest numbers in the data set.
• Step 2: Subtract the lowest number from the highest number.

Example: Let’s take the numbers: 4, 8, 15, 16, 23, 42.

• The highest number is 42.
• The lowest number is 4.
• The range is $42 - 4 = 38$.

So, the range is 38. This means there’s a wide spread of values.

2. Variance

Variance shows us how much the numbers differ from the average. Here’s how to calculate variance:

• Step 1: Find the mean (average) of the numbers.
• Step 2: Subtract the mean from each number and then square that result.
• Step 3: Find the average of all those squared numbers.

Example: Let’s use the same numbers (4, 8, 15, 16, 23, 42):

• First, find the mean: $(4 + 8 + 15 + 16 + 23 + 42) / 6 = 18$.
• Now, calculate the squared differences:
  • $(4 - 18)^2 = 196$
  • $(8 - 18)^2 = 100$
  • $(15 - 18)^2 = 9$
  • $(16 - 18)^2 = 4$
  • $(23 - 18)^2 = 25$
  • $(42 - 18)^2 = 576$.
• Add these up: $196 + 100 + 9 + 4 + 25 + 576 = 910$.
• Now, divide this sum by the number of values (6): $910 / 6 = 151$.

3. Standard Deviation

The standard deviation is the square root of the variance. It also helps us see how spread out the numbers are, using the same units as the original data.

Calculation:

$$\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{151} \approx 12.25$$

Visual Aids

Using graphs or number lines can help make these ideas clearer. By marking the data points and the average, you can visually see how spread out the numbers are.

By using these simple steps, Year 1 students can easily figure out range, variance, and standard deviation. This will help them build a strong base in statistics for their future learning!