13.3 Variance and Standard Deviation

Ask AI

Solved Examples

  1. Mean (xˉ\bar{x}): 6+8+10+12+145=505=10\frac{6+8+10+12+14}{5} = \frac{50}{5} = 10.
  2. Deviations (xi−10)(x_i - 10): −4,−2,0,2,4-4, -2, 0, 2, 4.
  3. Squared Deviations (xi−10)2(x_i - 10)^2: 16,4,0,4,1616, 4, 0, 4, 16.
  4. Sum of Squares: 16+4+0+4+16=4016+4+0+4+16 = 40.
  5. Variance (σ2\sigma^2): 405=8\frac{40}{5} = 8.
  6. Standard Deviation (σ\sigma): 8=22≈2.828\sqrt{8} = 2\sqrt{2} \approx 2.828.

Interactive Solver