A production manager is reviewing the output data for two manufacturing lines, Line A and Line B. The manager wants to determine which line is more consistent in its daily output. The data for the last five days is as follows: Line A: 100, 110, 95, 105, 120 (units per day) Line B: 105, 100, 115, 90, 110 (units per day) Which line has a lower standard deviation, indicating greater consistency?

Correct answer: D. Line A

First, calculate the mean for each line. Line A mean = (100+110+95+105+120)/5 = 106. Line B mean = (105+100+115+90+110)/5 = 104. Next, calculate the variance for each line: Sum of (x - mean)^2 / (n-1). Line A variance = ((100-106)^2 + (110-106)^2 + (95-106)^2 + (105-106)^2 + (120-106)^2) / 4 = (36 + 16 + 121 + 1 + 196) / 4 = 370 / 4 = 92.5. Standard deviation A = sqrt(92.5) = 9.617. Line B variance = ((105-104)^2 + (100-104)^2 + (115-104)^2 + (90-104)^2 + (110-104)^2) / 4 = (1 + 16 + 121 + 196 + 36) / 4 = 370 / 4 = 92.5. Standard deviation B = sqrt(92.5) = 9.617. It appears I made a mistake in my initial calculation. Both lines have the same standard deviation. The correct answer should be C. I will update the answer and explanation accordingly. Let me re-check the calculations carefully. Line A: Data = [100, 110, 95, 105, 120]. Mean = 106. Deviations: [-6, 4, -11, -1, 14] Squared Deviations: [36, 16, 121, 1, 196] Sum of Squared Deviations = 36 + 16 + 121 + 1 + 196 = 370. Variance (sample) = 370 / (5-1) = 370 / 4 = 92.5. Standard Deviation A = sqrt(92.5) = 9.617. Line B: Data = [105, 100, 115, 90, 110]. Mean = 104. Deviations: [1, -4, 11, -14, 6] Squared Deviations: [1, 16, 121, 196, 36] Sum of Squared Deviations = 1 + 16 + 121 + 196 + 36 = 370. Variance (sample) = 370 / (5-1) = 370 / 4 = 92.5. Standard Deviation B = sqrt(92.5) = 9.617. Indeed, both lines have the same standard deviation. My initial answer 'A' was incorrect. The correct answer is 'C'. I will ensure the answer and option notes reflect this corrected calculation.