10 Fig. 10.1 shows a sample collected from the large data set.
BMI is defined as \(\frac { \text { mass of person in kilograms } } { \text { square of person's height in metres } }\).
\begin{table}[h]
| Sex | Age in years | Mass in kg | Height in cm | BMI |
| Male | 38 | 77.6 | 164.8 | 28.57 |
| Male | 17 | 63.5 | 170.3 | 21.89 |
| Male | 18 | 68.0 | 172.3 | 22.91 |
| Male | 18 | 57.2 | 172.2 | 19.29 |
| Male | 19 | 77.6 | 191.2 | 21.23 |
| Male | 24 | 72.7 | 177.0 | 23.21 |
| Male | 25 | 92.5 | 177.9 | 29.23 |
| Male | 26 | 70.4 | 159.4 | 27.71 |
| Male | 31 | 77.5 | 174.0 | 25.60 |
| Male | 34 | 132.4 | 182.2 | 39.88 |
| Male | 38 | 115.0 | 186.4 | 33.10 |
| Male | 40 | 112.1 | 171.7 | 38.02 |
\captionsetup{labelformat=empty}
\caption{Fig. 10.1}
\end{table}
- Calculate the mass in kg of a person with a BMI of 23.56 and a height of 181.6 cm , giving your answer correct to 1 decimal place.
Fig. 10.2 shows a scatter diagram of BMI against age for the data in the table. A line of best fit has also been drawn.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c08a2212-3104-425e-8aee-7f2d46f23924-09_682_1212_351_248}
\captionsetup{labelformat=empty}
\caption{Fig. 10.2}
\end{figure} - Describe the correlation between age and BMI.
- Use the line of best fit to estimate the BMI of a 30-year-old man.
- Explain why it would not be sensible to use the line of best fit to estimate the BMI of a 60-year-old man.
- Use your knowledge of the large data set to suggest two reasons why the sample data in the table may not be representative of the population.
- Once the data in the large data set had been cleaned there were 196 values available for selection. Describe how a sample of size 12 could be generated using systematic sampling so that each of the 196 values could be selected in the sample.