Lecture on Standard Deviation

Overview

• Importance of standard deviation in data collection.
• Understanding standard deviation conceptually and calculating it by hand and using a spreadsheet.

Understanding Standard Deviation

• Related to the normal distribution (bell-shaped curve).
• Measures the spread or variation of data.
• Key Concept:
  • In a normal distribution:
    • 68% of data falls within one standard deviation from the mean.
    • 95% falls within two standard deviations.
    • 99% falls within three standard deviations.

Calculation of Standard Deviation

• Example Calculation:
  • Data set: 1, 2, 3, 4, 5
  • Steps:
    1. Calculate the mean (average):
       • Add all data points (1+2+3+4+5 = 15).
       • Divide by number of data points (5): Mean = 3.
    2. Calculate deviation for each data point:
       • (X - Mean)^2 for each data point.
       • Examples:
         • (1 - 3)^2 = 4
         • (2 - 3)^2 = 1
         • (3 - 3)^2 = 0
         • (4 - 3)^2 = 1
         • (5 - 3)^2 = 4
    3. Sum of squared deviations: 4 + 1 + 0 + 1 + 4 = 10.
    4. Divide by degrees of freedom (n-1): 10 / 4 = 2.5.
    5. Take the square root: √2.5 = 1.58.

Using Spreadsheets

• Example Data Set: 0, 2, 4, 5, 7
• Steps:
  • Enter data into spreadsheet cells.
  • Use functions to calculate:
    • Mean: =AVERAGE(range)
    • Standard Deviation: =STDEV(range)
  • Example result for standard deviation: 2.7, indicating a higher spread in data.

Conclusion

• Standard deviation is a crucial statistical tool for understanding data spread.
• Calculating by hand helps with understanding, while spreadsheets offer efficiency.
• Practice calculating both manually and with technological tools to strengthen understanding.