[ Mathematical Statistics ]

To serve on a submarine, a sailor's height must not exceed 168 cm. There are four teams A, B, C, and D. All sailors in these teams want to serve on a submarine and have passed a strict selection process. The final selection is based on height.

In team A, the average height of the sailors is 166 cm.

In team B, the median height of the sailors is 167 cm.

In team C, the tallest sailor has a height of 169 cm.

In team D, the mode of the sailors' heights is 167 cm.

In which team can at least half of the sailors definitely serve on a submarine?
Counterexample for Team A: three sailors with heights of 160, 169, and 169 cm. The average height is 166 cm, but two out of three are not fit for service on a submarine.

Counterexample for Team B: two sailors with heights of 169 cm. Neither can serve on the submarine. Team B also does not provide an answer to the question.

Counterexample for Team G: five sailors with heights of 167, 167, 169, 170, and 171 cm. The mode is 167, but three out of five cannot serve on the submarine.

Consider Team B. By definition of the median, not less than half of the sailors have a height of no more than 167 cm. These sailors can serve on a submarine. Perhaps there are also those whose height is exactly 168. Thus, at least half of the sailors in Team B can serve on a submarine.

## Answer

Team B.