Advanced Math Topics 6.4 Computational Formula for Variation and Standard Deviation

Variance: σ 2 = Σ(x – μ) 2 p(x) Do you remember the variance formula?

A bowling ball manufacturer makes bowling balls in 2 pound intervals from 8 to 18 pounds. The probability that a customer will buy a particular weighted ball is shown. Find the mean, variance, and standard deviation. x (lbs.)p(x) x p(x)x - μ(x – μ) 2 (x – μ) 2 p(x) – 12.6 = (21.16)(0.11) = – 12.6 = (6.76)(0.21) = – 12.6 = (0.36)(0.28) = – 12.6 = (1.96)(0.17) = – 12.6 = (11.56)(0.13) = – 12.6 = (29.16)(0.10) = σ 2 = Σ(x – μ) 2 p(x) μ = 12.6 σ 2 = σ = √ ≈ Do you remember this example?

A bowling ball manufacturer makes bowling balls in 2 pound intervals from 8 to 18 pounds. The probability that a customer will buy a particular weighted ball is shown. Find the mean, variance, and standard deviation. x (lbs.)p(x) x p(x)x 2 x 2 p(x) (64)(0.11) = (100)(0.21) = (144)(0.28) = (196)(0.17) = (256)(0.13) = (324)(0.10) = 32.4 σ 2 = Σx 2 p(x) – μ 2 μ = σ = √8.6 ≈ There is a computational formula that will give you the same answer, despite a possible rounding difference. σ 2 = – (12.6) 2 = 8.6

3) Janet is a medical lab technician. The number of EEG’s that she takes daily and the associated probabilities are shown. Find the mean, variance, and standard deviation for the distribution. From the HW P. 306 x (EEG’s)p(x) μ = 3.9 σ 2 = – (3.9) 2 = 4.29 σ = √4.29 ≈ 2.07 sum = 19.5

P. 306 #3, 12, and 13; for #12 and 13, compute each using both formulas; Quiz tomorrow From the HW P. 306