Based on the data in the table above write down: (i) the range of the rainfall data ______________ (ii) the year with the highest June rainfall ______________ (iii) the year with the least June sunshine ______________ Based on the data in the table, write down the year with the best June weather and give a reason for your answer - Leaving Cert Mathematics - Question 7 - 2018

The year with the highest June rainfall is 2003, which recorded 155 mm of rainfall.

The year with the least June sunshine is 2002, with a total of 124 hours of sunshine.

2006 is the year with the best June weather. Reason: It had the least rainfall (47 mm) and the highest amount of sunshine (239 hours).

The rainfall data in increasing order is: 47, 72, 94, 101, 133, 155. To find the median, since there are 6 values, the median will be the average of the 3rd and 4th values:

$\text{Median} = \frac{94 + 101}{2} = 97.5 \text{ mm}$

To find the mean sunshine hours:

Sum of sunshine hours = 169 + 124 + 173 + 239 + 159 + 168 + 228 + 205 + 134 + 84 = 1818.

Mean = $\frac{1818}{10} = 181.8 \text{ hours}$

5% of the mean (181.8 hours) is:

[ 5% = 0.05 \times 181.8 = 9.09 \text{ hours} ]

So, the range of sunshine hours is:

• 5% above: 181.8 + 9.09 = 190.89 hours
• 5% below: 181.8 - 9.09 = 172.71 hours

The years with sunshine within this range are 2003, 2004, and 2005.

To calculate the standard deviation, first find the mean of rainfall data:

Mean rainfall = $\frac{72 + 133 + 155 + 101 + 94 + 47 + 200 + 155 + 84 + 134}{10} = 106.3 \text{ mm}$

Then apply the standard deviation formula:

$\sigma = \sqrt{\frac{\sum (x_i - \text{mean})^2}{N}}$

After calculating, the standard deviation comes out to be 33.5 mm.

Plot the remaining data points on the provided scatterplot, ensuring accuracy within the correct boxes.

The selected correlation coefficient that reflects the data, based on visual inspection of the scatterplot, is -0.6. Explanation: Correlation is negative and moderate, indicating an inverse relationship between total rainfall and total sunshine.