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 (\(\mu\)) of a dataset is calculated using the formula:

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

For the given ages of the players, the sum of the ages is \(297\) and the number of players (\(N\)) is \(11\). Thus, the mean is:

\[ \mu = \frac{297}{11} = 27.0 \]

The median is the middle value of a dataset when it is ordered. For a dataset with an odd number of observations, the median is the value at position \(\frac{N+1}{2}\).

The sorted ages are: \([22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]\).

The rank for the median is calculated as:

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

The value at position 6 is \(27\), so the median is:

\[ \text{Median} = 27 \]

The mode is the value that appears most frequently in a dataset. In this case, the ages are:

\([23, 27, 31, 22, 29, 24, 30, 28, 26, 25, 32]\)

The mode is \(23\) as it appears more frequently than any other number.

Final Answer