AP Bio Unit 0.5

Overview

This lecture explains standard deviation, its meaning in the context of normal distribution, and demonstrates how to calculate it both manually and using software.

Variation and Standard Deviation

• Variation is the difference in data values within and between groups.
• Standard deviation measures how spread out (varied) data points are from the mean (average).
• A normal distribution (bell curve) is symmetric and shows how data is distributed around the mean.

Bell Curve and Data Distribution

• In a normal distribution, the mean is at the center.
• About 68% of data falls within ±1 standard deviation of the mean.
• About 95% of data falls within ±2 standard deviations.
• About 99% of data falls within ±3 standard deviations.

Calculating Standard Deviation

• Formula: standard deviation = square root of [sum of squared differences from the mean ÷ (number of data points - 1)].
• Steps:
  1. Find the mean of the data set.
  2. Subtract the mean from each data point.
  3. Square each result.
  4. Add all squared differences.
  5. Divide by (number of data points minus one).
  6. Take the square root of that result.
• Example: For data 1, 2, 3, 4, 5, the mean is 3, and the standard deviation calculates to 1.58.

Interpreting Standard Deviation

• The mean is placed in the center of the bell curve.
• Add and subtract the standard deviation to the mean to find the range covering most data.
• For two standard deviations, repeat the process to cover 95% of data.

Using Technology

• Standard deviation can be quickly calculated in Google Sheets using the STDEV function.
• Understanding the concept is more important than doing manual calculations every time.

Key Terms & Definitions

• Standard Deviation — a measure of data spread or variability from the mean.
• Mean (Average) — sum of the data points divided by the number of points.
• Normal Distribution — a symmetric, bell-shaped curve showing data distribution.
• Summation (Σ) — adding together all specified values.

Action Items / Next Steps

• Practice calculating standard deviation by hand for one or two data sets.
• Use Google Sheets or similar programs to calculate standard deviation for larger data sets.
• Review the concepts of mean, variation, and normal distribution.