The frequency table below summarizes the volume of apple juice dispensed from vending machine $A$

Question

The frequency table below summarizes the volume of apple juice dispensed from vending machine $A$ for $50$ trials. Volume from $A$ ($x$ ml)Frequency $246 < x \le 248$$4$ $248 < x \le 250$$7$ $250 < x \le 252$$28$ $252 < x \le 254$$6$ $254 < x \le 256$$5$ For vending machine $A$, calculate the mean,[2] the standard deviation.[2] Another vending machine $B$ is used to dispense apple juice. The mean and standard deviation of the volumes of apple juice dispensed by vending machine $B$ is $251.36$ ml and $2.22$ ml respectively. The nominal volume of each cup of apple juice dispensed from these vending machines is $250$ ml. If you run a vending machine business, which machine would you buy? Explain your choice.[2] What is the range of volume dispensed by machine $A$?[1] Why is the standard deviation preferred over the range as a measure of the spread of data?[1]

Accepted Answer

(a)(i) Estimated $251.04$ ml. (a)(ii) Estimated $1.98$ ml. (b) Machine A: closer mean and smaller spread. (c)(i) Exact range unknown; $6<R<10$ ml. (c)(ii) Standard deviation uses all observations, whereas range uses only the extremes.

Volume from \(A\) (\(x\) ml)	Frequency
\(246 < x \le 248\)	\(4\)
\(248 < x \le 250\)	\(7\)
\(250 < x \le 252\)	\(28\)
\(252 < x \le 254\)	\(6\)
\(254 < x \le 256\)	\(5\)

Statistics - Mean and Standard Deviation for Grouped Data

Statistics - Mean and Standard Deviation for Grouped Data

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