Standard deviation

• What does Standard Deviation measure in a dataset?

  The average distance each data point is from the mean
• What does a Standard Deviation of 5 indicate in test scores?

  Scores are typically within 5 points of the mean
• What are the purposes of Standard Deviation?

  • Measure dispersion: Show how spread out data is
  • Compare sets: Assess consistency of different datasets
• How can a researcher use Standard Deviation to compare test scores between two schools?


  Compare the standard deviations of test scores
• What is the first step in calculating Standard Deviation?

  Find the mean of the data
• What do you do after finding the mean in the Standard Deviation calculation process?

  Subtract the mean from each data point
• What do you do with the differences after subtracting the mean?


  Square each difference
• How is variance calculated in the Standard Deviation process?

  Sum squared differences and divide by the number of data points
• What is the final step in calculating Standard Deviation?

  Take the square root of the variance
• What does a small Standard Deviation indicate about a dataset?

  Data is consistent and centered around the mean
• What does a large Standard Deviation suggest about a dataset?


  Data is spread out and less consistent
• How does Standard Deviation compare to Range and Interquartile Range (IQR)?


  • Range: Difference between max and min values
  • Standard Deviation: Average distance from mean, sensitive to all data points
  • IQR: Spread of middle 50%, ignores outliers
• What is the formula for Interquartile Range (IQR)?

  IQR = Q3 - Q1
• What does the IQR focus on in a dataset?

  The middle 50% of the data
• Why is IQR considered resistant to outliers?

  It focuses on the central 50% of data
• For the dataset $2, 4, 6, 8, 10, 12, 14, 16, 18$, what is the IQR?


  IQR = 14 - 6 = 8
• For the dataset $3, 4, 6, 7, 8$, what is the standard deviation rounded to two decimal places?


  $\sqrt{3.44} \approx 1.86$