<p>The frequency table below summarizes the volume of apple juice dispensed from vending machine \(A\) for&nbsp;\(50\) trials.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Volume from \(A\) (\(x\) ml)</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Frequency</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(246 &lt; x \le 248\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(4\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(248 &lt; x \le 250\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(7\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(250 &lt; x \le 252\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(28\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(252 &lt; x \le 254\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(6\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(254 &lt; x \le 256\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(5\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">For vending machine \(A\), calculate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the mean,</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the standard deviation.</span><span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">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.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">What is the range of volume dispensed by machine \(A\)?</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Why is the standard deviation preferred over the range as a measure of the spread of data?</span><span class="inline-marks">[1]</span></div></li></ol></li></ol>

The frequency table below summarizes the volume of apple juice dispensed from vending machine \(A\) for \(50\) trials.

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.

What is the range of volume dispensed by machine \(A\)?

Why is the standard deviation preferred over the range as a measure of the spread of data?

Statistics - Mean and Standard Deviation for Grouped Data

Question 18ee8ab8

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