- The stem and leaf diagram gives the blood pressure, \(x \mathrm { mmHg }\), for a random sample of 19 female patients.
| 10 | 1 | 2 | | | | | | | |
| 11 | 2 | 7 | 7 | 8 | 8 | | | | |
| 12 | 0 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 7 |
| 13 | 1 | 2 | 9 | | | | | | |
Key: 10 | 1 means blood pressure of 101 mmHg
- Find the median and the quartiles for these data.
- Find the interquartile range ( \(Q _ { 3 } - Q _ { 1 }\) )
An outlier is a value that is greater than \(Q _ { 3 } + 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\) or less than \(Q _ { 1 } - 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\)
- Showing your working clearly, identify any outliers for these data.
- On the grid on page 21 draw a box and whisker plot to represent these data. Show any outliers clearly.
The above data can be summarised by
$$\sum x = 2299 \text { and } \sum x ^ { 2 } = 279709$$
- Calculate the mean and the standard deviation for these data.
For a random sample taken from a normal distribution, a rule for determining outliers is: an outlier is more than \(2.7 \times\) standard deviation above or below the mean.
- Find the limits to determine outliers using this rule.
- State, giving a reason based on some of the above calculations, whether or not a normal distribution is a suitable model for these data.
\includegraphics[max width=\textwidth, alt={}, center]{8ff7539e-fa44-4388-af8c-80656f081528-21_2281_73_308_15}
Turn over for a spare diagram if you need to redraw your plot.
\includegraphics[max width=\textwidth, alt={}]{8ff7539e-fa44-4388-af8c-80656f081528-24_2639_1830_121_121}