Questions: The following table gives the value (in billions of dollars) of the 10 most valuable teams in a professional sports league. Team A B C D E F G H I J Value 4.30 3.50 3.20 3.00 2.93 2.90 2.74 2.70 2.50 2.40 (a) Find the mean. (b) Find the median. (a) The mean is billion. (Type an integer or a decimal.)

Solution Steps

To find the mean value of the team values, we use the formula:

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

where \( N \) is the number of teams and \( x_i \) are the values of the teams.

Calculating the sum:

\[ \sum_{i=1}^{10} x_i = 30.17 \]

Thus, the mean is:

\[ \mu = \frac{30.17}{10} = 3.02 \]

The mean value is: \( 3.02 \) billion.

To find the median, we first sort the team values:

\[ \text{Sorted data} = [2.4, 2.5, 2.7, 2.74, 2.9, 2.93, 3.0, 3.2, 3.5, 4.3] \]

Since there are \( N = 10 \) values (an even number), the median \( Q \) is calculated using the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (10 + 1) = 5.5 \]

This indicates that the median is the average of the 5th and 6th values in the sorted list:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{2.9 + 2.93}{2} = 2.915 \]

The median value is approximately \( 2.92 \) billion.

Final Answer