Question

The heights of five starting players on a basketball team have a mean of 76 inches, a median of 78 inches, and a range of 11 inches.

a. If the tallest of these five players is replaced by a substitute who is 2inches taller, find the mean, median, and range

b. If the tallest player is replaced by a substitute who is 4 inches shorter, which of the new values (mean, median, range) could you determine and what would their new values be?

Answer 1

a) As the tallest of the 5 players is substituted with a player 2 inches taller, therefore

New mean = Old Mean + 2/5 = 76 + 0.4 = 76.4 inches.

New Median = Old median, because the middle value wont change by changing the maximum value. Therefore new median = 78 inches.

New Range = Old Range + (new max - old max ) = 11 + 2 = 13 inches.

Therefore new range = 13 inches.

b) We can determine the new mean as:

New Mean = Old mean - 4/5 = 76 - 0.8 = 75.2 inches

New median cannot be computed here, as we are not sure about the position that the new value would have, the middle value may not remain the same.

New Range can again not be computed, because we would not know the maximum value after the substitution.