A.3 Answer: TW 3 tutorial
Answers for Sect. 3.2
- Some of the significant figures look ridiculous. Mean: \(990.0791\), or \(990.1\) tonnes. Standard deviation: \(1588.514579\), or \(1588.5\) tonnes. (Specifically, not \(1485.919327\).)
- Median: \(180.5\) tonnes.
- 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.
- Volume of drinks in \(375\,\text{mL}\): Graph D. (Students sometimes say Graph A, thinking that most cans have very similar amounts.)
- Time in exam for short or easy exam: Graph C.
- Time in exam for long or hard exam: Graph B.
- The heights of females UniSC students: Graph D.
- The starting salaries: Graph C. (Students sometimes say Graph B, thinking that salaries rise over time.)
Answers for Sect. 3.6
- Female Weddell: about \(260\)--\(270\,\text{cm}\) long, vary from about \(200\) to \(310\,\text{cm}\). Slight negative skewness; possible small outlier at about \(170\)--\(180\,\text{cm}\).
- Dotchart.
(Too much data for a useful stem-and-leaf plot probably.) - Better with a title; some more labelled tick marks would be better.
Answers for Sect. 3.7
- 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).
- Descriptive. \(\bar{x} = 102.62\,\text{MPa}\); \(s = 5.356\,\text{MPa}\). The median is \(101.1\,\text{MPa}\).
- 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
- Observational: the 'treatment' (brand of battery) is not assigned; we simply take measurements from the batteries that exist.
- Units of observation and units of analysis: The individual batteries.
- Energizer: mean: \(7.36\,\text{h}\); std dev: \(0.289\,\text{h}\). Ultracell: mean: \(7.41\,\text{h}\); std dev: \(0.172\,\text{h}\).
- Ultracell batteries are slightly better (last longer) on average, and more consistent performers.
- Energizer: median: \(7.46\,\text{h}\). Ultracell: median: \(7.48\,\text{h}\). So Ultracell batteries are slightly better (last longer) on average.
- Probably median (outliers?), but mean and median are similar in any case.
- 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. - At the time of the study, the Ultracell batteries were substantially cheaper, and hence much better value.