Fix the mistake: Data Analysis

Data Analysis ① Measures of Central Tendency and Dispersion

Measures of central tendency (mean, median, and mode) and dispersion (variance and standard deviation) are indicators that express the characteristics of data numerically.

Variance and Standard Deviation

Variance s² = Σ(xi - x̄)² / n
Standard deviation s = √(variance)
（x̄ is the mean, and n is the number of data values）

Example ①
Find the variance and standard deviation of the data: 2, 4, 6, 8.
Answer: Mean = 5. Variance = {(2-5)² + (4-5)² + (6-5)² + (8-5)²}/4 = (9+1+1+9)/4 = 5.
Standard deviation = √5.
Key Point
  • Variance = the mean of the squared deviations (xi - x̄)
  • Standard deviation = the positive square root of the variance
  • The greater the spread, the greater the variance and standard deviation

Practice Problems

  1. Find the mean, variance, and standard deviation of the data: 1, 3, 5, 7, 9.

Answers and Explanations

  1. Answer: Mean 5, variance 8, standard deviation 2√2. Deviations: -4,-2,0,2,4. Variance=(16+4+0+4+16)/5=8.

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