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The Grades In Mathematics Of The Students In Section A Are As Follows: 80, 75, 60, 95, 100. What Is The Populaton Mvariance Of Their Group?
The grades in mathematics of the students in section A are as follows: 80, 75, 60, 95, 100. What is the populaton mvariance of their group? Answer: The population variance is 206. Step-by-step explanation: Steps in solving for the population variance: 1) Find the mean by adding the values of (the grades in Math), then divide the sum by number of observations. Total Values (x): ∑x = (60 + 75 + 80 + 95 + 100) ∑x = 410 Population Mean: μ = ∑x/N Where N = 5 μ =410/5 μ = 82 2) Subtract the mean from each x ⇒ (x - μ): 60 – 82 = - 22 75 – 82 = -7 80 – 82 = -2 95 – 82 = 13 95 – 82 = 18 3.) Square each difference between x and mean ⇒ (x - μ)²: (-22)2 = 484 (-7)2 = 49 (-2)2 = 4 (13)2 = 169 (18)2 = 324 4.) Add the results in #3: ∑(x - μ)² = (484 + 49 + 4 + 169 + 324) ∑(x - μ)² = 1,030 5.) Solve of the population variance (σ) by dividing the sum in #4 by the number of observations (N): Population Variance: σ² = ∑(x - μ)² / N σ² = 1,030/5 σ² = 206 Please click the i
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