Page 2: Calculating Standard Deviation Step-by-Step

This page provides a detailed, step-by-step guide on how to calculate standard deviation using a real-world example of holly leaf measurements.

The calculation process is broken down into the following steps:

1. Calculate the mean of the dataset
2. Subtract the mean from each data point to find (x-x̄)
3. Square each difference (x-x̄)²
4. Sum all the squared differences Σ(x-x̄)²
5. Divide the sum by (n-1), where n is the number of data points
6. Calculate the square root of the result

Example: For holly leaves collected at 0.5m height:

• Mean = 9.3 cm
• Σ(x-x̄)² = 8.1
• n = 10
• S = √[8.1 / (10-1)] = 0.95 cm (rounded to two decimal places)

Highlight: The standard deviation for leaves collected at 0.5m height is approximately 0.95 cm, indicating the typical variation in leaf length at this height.

The page emphasizes the importance of following each step carefully to ensure accurate results when calculating standard deviation manually.

Vocabulary:

• Σ (sigma) represents the sum of values
• (n-1) is used instead of n to provide an unbiased estimate of population standard deviation when working with a sample

This detailed breakdown helps students understand the process of calculating standard deviation and interpreting its meaning in real-world contexts.