Question

Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14. The answer should have two decimals.

Please show your work.

Answer 1

n = 9

X = mean = (4+9+11+12+17+5+8+12+14) / 9 = 92 / 9 = 10.2222

Variance = Σ(x - X)^2 / n

= [(4-10.2222)^2 + (9-10.2222)^2 + (11-10.2222)^2 + (12-10.2222)^2 + (17-10.2222)^2 + (5-10.2222)^2 + (8-10.2222)^2 + (12-10.2222)^2 + (14-10.2222)^2] / 9

= [38.7157728 + 1.49377284 + 0.60497284 + 3.16057284 + 45.93857284 + 27.27137284 + 4.93817284 + 3.16057284 + 14.27177284] / 9

= 139.5555556 / 9

= 15.50617284

Standard deviaiton = Squareroot of variance

= (15.50617284)^(1/2)

= 3.93778781

Therefore, standard deviation os 3.94