CORE, FUR2 2016 VCAA 2
A weather station records daily maximum temperatures
- The five-number summary for the distribution of maximum temperatures for the month of February is displayed in the table below.
- The boxplots below display the distribution of maximum daily temperature for the months of May and July.
- Describe the shapes of the distributions of daily temperature (including outliers) for July and for May. (1 mark)
- Determine the value of the upper fence for the July boxplot. (1 mark)
- Using the information from the boxplots, explain why the maximum daily temperature is associated with the month of the year. Quote the values of appropriate statistics in your response. (1 mark)
- Describe the shapes of the distributions of daily temperature (including outliers) for July and for May. (1 mark)
CORE, FUR2 2006 VCAA 1
Table 1 shows the heights (in cm) of three groups of randomly chosen boys aged 18 months, 27 months and 36 months respectively.
- Complete Table 2 by calculating the standard deviation of the heights of the 18-month-old boys.
Write your answer correct to one decimal place. (1 mark)
A 27-month-old boy has a height of 83.1 cm.
- Calculate his standardised height (`z` score) relative to this sample of 27-month-old boys.
Write your answer correct to one decimal place. (1 mark)
The heights of the 36-month-old boys are normally distributed.
A 36-month-old boy has a standardised height of 2.
- Approximately what percentage of 36-month-old boys will be shorter than this child? (1 mark)
Using the data from Table 1, boxplots have been constructed to display the distributions of heights of 36-month-old and 27-month-old boys as shown below.
- Complete the display by constructing and drawing a boxplot that shows the distribution of heights for the 18-month-old boys. (2 marks)
- Use the appropriate boxplot to determine the median height (in centimetres) of the 27-month-old boys. (1 mark)
The three parallel boxplots suggest that height and age (18 months, 27 months, 36 months) are positively related.
- Explain why, giving reference to an appropriate statistic. (1 mark)