(i) To find the mean height of the remaining group of 27 people, we use the formula for the mean:

\(\text{New mean} = \frac{172.6 \times 28 - 161.8}{27} = 173 \text{ cm}\)

(ii) First, find \(\Sigma x^2\) for the original group of 28 people using the formula:

\(\Sigma x^2 = (4.58^2 + 172.6^2) \times 28 = 834728.6\)

Then, for the remaining group of 27 people:

\(\text{Remaining } \Sigma x^2 = 834728.6 - 161.8^2 = 808549.36\)

Finally, calculate the standard deviation for the remaining group:

\(\text{sd of remaining} = \sqrt{\frac{808549.36}{27} - 173^2} = 4.16 \text{ cm}\)