4 Farfield Travel and Lacket Travel are two travel companies which arrange tours abroad. The numbers of holidays arranged in a certain week are recorded in the table below, together with the means and standard deviations of the prices.
| | | | Standard | | deviation \)( \\( )\) |
|
| Farfield Travel | 30 | 1500 | 230 |
| Lacket Travel | 21 | 2400 | 160 |
- Calculate the mean price of all 51 holidays.
- The prices of individual holidays with Farfield Travel are denoted by \(
) x _ { F }\( and the prices of individual holidays with Lacket Travel are denoted by \)\\( x _ { L }\). By first finding \(\Sigma x _ { F } ^ { 2 }\) and \(\Sigma x _ { L } ^ { 2 }\), find the standard deviation of the prices of all 51 holidays.