1 The average maximum monthly temperatures, \(u\) degrees Fahrenheit, and the average minimum monthly temperatures, \(v\) degrees Fahrenheit, in New York City are as follows.
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
| Maximum (u) | 39 | 40 | 48 | 61 | 71 | 81 | 85 | 83 | 77 | 67 | 54 | 41 |
| Minimum (v) | 26 | 27 | 34 | 44 | 53 | 63 | 68 | 66 | 60 | 51 | 41 | 30 |
- Calculate, to one decimal place, the mean and the standard deviation of the 12 values of the average maximum monthly temperature.
- For comparative purposes with a UK city, it was necessary to convert the temperatures from degrees Fahrenheit ( \({ } ^ { \circ } \mathrm { F }\) ) to degrees Celsius ( \({ } ^ { \circ } \mathrm { C }\) ). The formula used to convert \(f ^ { \circ } \mathrm { F }\) to \(c ^ { \circ } \mathrm { C }\) is:
$$c = \frac { 5 } { 9 } ( f - 32 )$$
Use this formula and your answers in part (a)(i) to calculate, in \({ } ^ { \circ } \mathbf { C }\), the mean and the standard deviation of the 12 values of the average maximum monthly temperature.
(3 marks)
- The value of the product moment correlation coefficient, \(r _ { u v }\), between the above 12 values of \(u\) and \(v\) is 0.997 , correct to three decimal places.
State, giving a reason, the corresponding value of \(r _ { x y }\), where \(x\) and \(y\) are the exact equivalent temperatures in \({ } ^ { \circ } \mathrm { C }\) of \(u\) and \(v\) respectively.
(2 marks)