The table below shows the total rainfall, in millimetres, and the total sunshine, in hours, at Valentia, County Kerry, during the month of June from 2001 to 2010 - Leaving Cert Mathematics - Question 7 - 2018

The year with the highest June rainfall is 2007, with total rainfall of 149 mm.

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

The year with the best June weather is 2006 because it had the least rainfall (47 mm) and the highest number of sunshine hours (159 hours), indicating more sunny days.

The rainfall data in increasing order is:

47, 72, 84, 94, 101, 133, 149, 155

There are a total of 8 values, so the median is the average of the 4th and 5th values:

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

To find the mean, sum the total sunshine hours and divide by the number of years:

$\text{Mean} = \frac{169 + 124 + 180 + 173 + 239 + 159 + 168 + 228 + 205}{10} = \frac{1818}{10} = 181.8 \text{ hours}$

5% of the mean sunshine hours (181.8) is:

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

The range within 5% of the mean is:

• Lower limit: 181.8 - 9.09 = 172.71 hours
• Upper limit: 181.8 + 9.09 = 190.89 hours

The years where sunshine data falls within this range are 2003, 2004, and 2005.

First, we calculate the mean rainfall:

$\text{Mean} = \frac{72 + 133 + 155 + 101 + 94 + 47 + 149 + 134 + 94 + 84}{10} = \frac{1,170}{10} = 117.0 \text{ mm}$

Then, calculate the variance:

$\sigma^2 = \frac{(72 - 117)^2 + (133 - 117)^2 + ... + (84 - 117)^2}{10} = 1111.6$

Finally, the standard deviation is:

$\sigma = \sqrt{1111.6} \approx 33.3 \text{ mm}$ (down to 1 decimal place)

The remaining data points to plot are:

• (133 mm, 124 hours)
• (155 mm, 180 hours)
• (101 mm, 173 hours)
• (94 mm, 239 hours)
• (149 mm, 168 hours)
• (134 mm, 228 hours)
• (94 mm, 205 hours)

Make sure to plot these points accurately on the scatterplot accordingly.

Based on visual assessment of the scatterplot, I believe the most accurate reflection of the correlation coefficient is -0.6. This indicates a negative and moderate correlation between total rainfall and total sunshine hours, suggesting that as rainfall increases, sunshine hours tend to decrease.