(i) To find the mean price of all 51 holidays, use the formula for the combined mean:

\(\text{Mean} = \frac{30 \times 1500 + 21 \times 2400}{51} = \frac{45000 + 50400}{51} = 1870.59\)

Rounding to 3 significant figures, the mean is 1870.

(ii) First, find \(\sum x_F^2\) and \(\sum x_L^2\) using the given standard deviations and means:

For Farfield Travel:

\(230^2 = \frac{\sum x_F^2}{30} - 1500^2\)

\(\sum x_F^2 = 30 \times (230^2 + 1500^2) = 69\,087\,000\)

For Lacket Travel:

\(160^2 = \frac{\sum x_L^2}{21} - 2400^2\)

\(\sum x_L^2 = 21 \times (160^2 + 2400^2) = 121\,497\,600\)

\(Now, calculate the combined variance:\)

\(\text{New variance} = \frac{69\,087\,000 + 121\,497\,600}{51} - 1870.59^2 = 237\,853\)

\(The standard deviation is the square root of the variance:\)

\(\text{New standard deviation} = \sqrt{237\,853} \approx 488\)