The population variance of the capacities is 30.76
the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151.
The number of observations n = 10
mean = (x₁ + x₂ + x₃.....x₁₀)/10
mean = (140 + 136 + 150 + 144 + 148 + 152 + 138+ 141 + 143 + 151)/10
mean = 1443/10 = 144.3
variance = ∑(x - mean)²/(n - 1)
variance = ((140 - 144.3)² + (136 - 144.3)² + (150 - 144.3)² + (144- 144.3)² + (148 - 144.3)² + (152 - 144.3)² + (138 - 144.3)² + (141-144.3)² + (143 - 144.3)² + (151 - 144.3)²)/(10 - 1)
variance = 276.9/9 = 30.76
Therefore, the population variance of the capacities is 30.76
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