## A.4 Answers to Teaching Week 4 tutorial

1. The smallest jellyfish has a breadth of (approx.) 6mm. A median of 4mm is silly! The median is somewhere between 8 and 10mm

2. A typical Dangar Island jellyfish has a breadth of about 10mm, but the variation is from about 6 to 16mm. The data are slightly skewed to the right (most jellyfish have smaller breadths, but some have larger breadths), but the shape is a bit funny (more data would smooth it out).

3. Site A is Dangar Island.

Jellyfish at Salamander Bay generally have a larger breadth: The median breadth at Salamander Bay (about 16mm) is greater than almost all the jellyfish at Dangar Island.

Jellyfish at Salamander Bay are a little less variable in terms of breadth. The distributions look slightly skewed right at both sites.

1. Descriptive RQ.
2. $$\bar{x}=102.62$$MPa; $$s=5.356$$MPa.
3. The median is $$101.1$$MPa. The range is from $$97.6$$ to $$111.2$$, or $$13.6$$MPa.
4. Report none based on five values! Too few data points! In any case, both the median and the mean have very similar values.
5. If all five measurements came from one board, we would not have a good representation of 'bamboo floorboards' in general. We would have just one unit of analysis.

1. Median largest: Class D
2. Median smallest: Class C
3. Standard deviation largest: Class A
4. Standard deviation smallest: Class D

1. A few issues...
• Five decimal places is to the nearest 0.01 of a mm!
• The standard deviation of the difference is not the difference between the individual standard deviations.
• A standard deviation cannot be negative. (Same applies to standard errors, but we aren't there yet.)
• Note that there is a sample size of 0 for the difference!
2. A few issues...
• Five decimal places: That's accuracy to 0.00001 of a millimetre per second. I don't think so...
• There is no numerical measures of the most important thing and the thing the RQ (presumably) concerns:
• The differences between the two brands.

### A.4.1 Answers to Sect. 4.7

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: $$7.36$$ hours; std dev: $$0.289$$. Ultracell: mean: $$7.41$$ hours; std dev: $$0.172$$. So Ultracell batteries are slightly better (last longer) on average, and more consistent performers. 4. Energizer: median: 7.46 hours. Ultracell: median: 7.48 hours. So Ultracell batteries are slightly better (last longer) on average. 5. Probably median (outliers?), but mean and median are similar in any case. 6. Values are close. Certainly no practically importance difference. 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. But in practical terms, the difference is minimal. (Based on means, the difference is 0.05 hrs, or 3 mins in over 7 hrs use! Based on medians, the difference is 0.02 hours, or 1.2 mins!) The practical difference is negligible. 7. Quite possibly, some very low values for both brands. 8. Yes: At the time of the study, the Ultracell batteries were substantially cheaper, and hence much better value.

### A.4.2 Answers to Sect. 4.8

FAS here is about 20--25 in general, ranging from 10 to 50 (which are actually the smallest and largest possible scores). Here's is a detailed explanation. You are not expected to go to this detail! The FAS is about 25 on average, ranging from about 10 to 50, slightly skewed right with no outliers. The distribution is unimodal. (The heights of the bars are, as best as I can figure, 3; 14; 44; 34; 22; 17; 5; 3.) With $$n=142$$, the median is observation number 71.5, which is in the 25--30 bar. The quartiles will have about 35 in them, so $$Q_1$$ will be in the 20--25 bar, and $$Q_3$$ will be in the 30--35 bar. Histogram is pretty good; bars really should be touching.

### A.4.3 Answers to Sect. 4.9

The median temperatures similar; a slight increase from Office A to C. IQR similar for each office, and range similar for Offices A and C (slightly larger for Office B).

### A.4.4 Answers to Sect. 4.9

1. Not shown. 2. Office a a bit different (cooler) on average. 3. Perhaps Office A.

### A.4.5 Answers to Sect. 4.10

1. Stacked or side-by-side barcharts; whether bird injured or not, and whether upper or lower are both qualitative variables. 2. Boxplots would be OK; one quantitative (length-of-stay) and one qualitative (therapy type) variable. 3. Scatterplots; two quantitative variables (frequency; amount wheat consumed).
4. Two-way table or stacked/side-by-side barchart, or table; two qualitative variables vars (30 mins of physical activity or not; vigorous physical activity or not).

### A.4.6 Answers to Sect. 4.11

1. Mean: 168.5714, or 168.57 m. Standard deviation: 6.966279, or 6.97 m. (Specifically, it is not 6.44952.) The median: 169.9 m. 2. Mean: 990.0791, or 990.079 tonnes. Standard deviation: 1588.514579, or 1588.5146 tonnes. (Specifically, it is not 1485.919327.) Median: 180.516 tonnes. 3. Mean: 13.88778, or 13.888%. Standard deviation: 2.617402, or 2.617%. Median: 13.35%.