There are \(9\) people in the Pin Pals bowling club. After a game one night, the scores for each player were \(157\), \(153\), \(159\), \(161\), \(153\), \(151\), \(156\), \(157\), and \(154\). During the game, the players were split between two lanes: Lane 1 and Lane 2. The following information is known about the scores of the players in each of the lanes.
No player in Lane 1 scored higher than any player in Lane 2. However, one player in Lane 1 had the same score as a player in Lane 2.
Two of the players in Lane 1 had the same score.
Determine the difference between the mean score of the players in Lane 1 and the mean score of the players in Lane 2.
This problem was inspired by a past Beaver Computing Challenge (BCC) problem.
Themes: Data Management, Number Sense