Questions: Listed below are the ages of 11 players randomly selected from the roster of a championship sports team. Find the (a) mean, (b) median, (c) mode, and (d) midrange and then (e) determine how the resulting statistics are fundamentally different from those calculated from the jersey numbers of the same 11 players.

Solution Steps

The mean age \( \mu \) is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of players and \( x_i \) represents the ages of the players. For the given ages:

\[ \mu = \frac{286}{11} = 26.0 \]

Thus, the mean age is \( 26.0 \) years.

To find the median, we first sort the ages:

\[ \text{Sorted data} = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] \]

The median is the value at the position calculated by:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (11 + 1) = 6.0 \]

The median corresponds to the value at position 6, which is \( 26 \). Therefore, the median age is \( 26 \) years.

The mode is the value that appears most frequently in the dataset. In this case, the mode age is \( 24 \) years.

Final Answer