6 The maximum temperatures \(x\) degrees Celsius recorded during each month of 2005 in Cambridge are given in the table below.
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
| 9.2 | 7.1 | 10.7 | 14.2 | 16.6 | 21.8 | 22.0 | 22.6 | 21.1 | 17.4 | 10.1 | 7.8 |
These data are summarised by \(n = 12 , \Sigma x = 180.6 , \Sigma x ^ { 2 } = 3107.56\).
- Calculate the mean and standard deviation of the data.
- Determine whether there are any outliers.
- The formula \(y = 1.8 x + 32\) is used to convert degrees Celsius to degrees Fahrenheit. Find the mean and standard deviation of the 2005 maximum temperatures in degrees Fahrenheit.
- In New York, the monthly maximum temperatures are recorded in degrees Fahrenheit. In 2005 the mean was 63.7 and the standard deviation was 16.0 . Briefly compare the maximum monthly temperatures in Cambridge and New York in 2005.
The total numbers of hours of sunshine recorded in Cambridge during the month of January for each of the last 48 years are summarised below.
| Hours \(h\) | \(70 \leqslant h < 100\) | \(100 \leqslant h < 110\) | \(110 \leqslant h < 120\) | \(120 \leqslant h < 150\) | \(150 \leqslant h < 170\) | \(170 \leqslant h < 190\) |
| Number of years | 6 | 8 | 10 | 11 | 10 | 3 |
- Draw a cumulative frequency graph for these data.
- Use your graph to estimate the 90th percentile.