A soft-drink bottling company fills and ships soda in plastic bottles with a target volume of 354 milliliters. The filling machinery does not deliver a perfectly consistent volume of liquid to each bottle, and the three quartiles for the fill volume are $Q _ { 1 } = 351 , Q _ { 2 } = 355$ and $Q _ { 3 } = 357$
A fill volume of 353 mL is considered low. Would a fill volume of 353 mL be considered an outlier?

Question

A soft-drink bottling company fills and ships soda in plastic bottles with a target volume of 354 milliliters. The filling machinery does not deliver a perfectly consistent volume of liquid to each bottle, and the three quartiles for the fill volume are $Q _ { 1 } = 351 , Q _ { 2 } = 355$ and $Q _ { 3 } = 357$
A fill volume of  353 mL is considered low. Would a fill volume of  353 mL  be considered an outlier?

Quizplus · Accepted Answer

A fill volume of 353 mL would not be considered an outlier because it falls within the range defined by the interquartile range (IQR). The IQR is calculated as $Q_3 - Q_1 = 357 - 351 = 6$. Outliers are typically defined as observations that fall more than 1.5 times the IQR above the third quartile or below the first quartile. In this case, the lower bound for outliers would be $Q_1 - 1.5 \times IQR = 351 - 1.5 \times 6 = 342$, and the upper bound would be $Q_3 + 1.5 \times IQR = 357 + 1.5 \times 6 = 366$. Since 353 falls within the range of 342 to 366, it is not considered an outlier.

A Soft-Drink Bottling Company Fills and Ships Soda in Plastic Q1=351,Q2=355Q _ { 1 } = 351 , Q _ { 2 } = 355Q1​=351,Q2​=355

A Soft-Drink Bottling Company Fills and Ships Soda in Plastic $Q _ { 1 } = 351 , Q _ { 2 } = 355$