A.3 Answer: TW 3 tutorial

Answers for Sect. 3.2

  1. Some of the significant figures look ridiculous. Mean: \(990.0791\), or \(990.1\) tonnes. Standard deviation: \(1588.514579\), or \(1588.5\) tonnes. (Specifically, not \(1485.919327\).)
  2. Median: \(180.5\) tonnes.
  3. Splitting the data into two parts of four observations each: \(Q_1\) is half-way between \(8.0001\) and \(29.4\) tonnes: \(Q_1 = 18.7005\). \(Q_3\) is half-way between \(676.2\) and \(2547.3\) tonnes: \(Q_1 = 1611.75\). The IQR is \(1611.75 - 18.7005 = 1593.05\), or about \(1593\) tonnes.

Answers for Sect. 3.3

Answers implied by H5P. Median largest: Class D. Median smallest: Class C. Standard deviation largest: Class A. Standard deviation smallest: Class D.

Answers for Sect. 3.4

Answers implied by H5P.

  1. Volume of drinks in \(375\,\text{mL}\): Graph D. (Students sometimes say Graph A, thinking that most cans have very similar amounts.)
  2. Time in exam for short or easy exam: Graph C.
  3. Time in exam for long or hard exam: Graph B.
  4. The heights of females UniSC students: Graph D.
  5. The starting salaries: Graph C. (Students sometimes say Graph B, thinking that salaries rise over time.)

Answers for Sect. 3.6

  1. Female Weddell: about \(260\)--\(270\,\text{cm}\) long, vary from about \(200\) to \(310\,\text{cm}\). Slight negative skewness; possible small outlier at about \(170\)--\(180\,\text{cm}\).
  2. Dotchart.
    (Too much data for a useful stem-and-leaf plot probably.)
  3. Better with a title; some more labelled tick marks would be better.

Answers for Sect. 3.7

  1. Mean: \(168.5714\), or \(168.57\,\text{m}\). Standard deviation: \(6.966279\), or \(6.97\,\text{m}\). (Specifically, not \(6.44952\).) Median: \(167.9\,\text{m}\). IQR: \(175.0 - 162.5 = 12.5\,\text{m}\) (software may give a different value).
  2. Descriptive. \(\bar{x} = 102.62\,\text{MPa}\); \(s = 5.356\,\text{MPa}\). The median is \(101.1\,\text{MPa}\).
  3. Mean: \(13.88778\), or \(13.888\)%. Standard deviation: \(2.617402\), or \(2.617\)%. Median: \(13.35\)%. IQR: \(16.115 - 11.66 = 4.455\)% (software may give a different value).

Answers for Sect. 3.8.1

  1. Observational: the 'treatment' (brand of battery) is not assigned; we simply take measurements from the batteries that exist.
  2. Units of observation and units of analysis: The individual batteries.
  3. Energizer: mean: \(7.36\,\text{h}\); std dev: \(0.289\,\text{h}\). Ultracell: mean: \(7.41\,\text{h}\); std dev: \(0.172\,\text{h}\).
  4. Ultracell batteries are slightly better (last longer) on average, and more consistent performers.
  5. Energizer: median: \(7.46\,\text{h}\). Ultracell: median: \(7.48\,\text{h}\). So Ultracell batteries are slightly better (last longer) on average.
  6. Probably median (outliers?), but mean and median are similar in any case.
  7. Values are close.
    Energizer batteries take, on average, less time to reach \(1.0\) volts, so are 'worse' in this regard. They also have a lot more variation. (Based on means, the difference is \(0.05\,\text{h}\), or \(3\,\text{mins}\) in over \(7\,\text{h}\) use! Based on medians, the difference is \(0.02\,\text{h}\), or \(1.2\,\text{mins}\)!) The practical difference is negligible.
  8. At the time of the study, the Ultracell batteries were substantially cheaper, and hence much better value.
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