Question

The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100 What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students? a0 What is the standard deviation, to the nearest tenth, of the data if the scores represent the entire population of Mr. Smith's students?

Answer 1

Mean: xbar = (∑i=1...10 xi)/10 = (61 + ... + 100)/10 = 84.4 Sum Of Squares in X SSX = ∑i (x - xbar)2 = (61 - 84.4)2 + ... + (100 - 84.4)2 = 1364.4 Standard deviation Sample: s = √[SSX / (10 - 1)] ≈ 12.3 Population: σ = √(SSX / 10) ≈ 11.7