Questions: The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set 2, 8, 15, 5, 14, 7, 12, 8, 3, 0 The range is 13 The population mean is 32 . The population variance is .

Solution Steps

The range is calculated as the difference between the maximum and minimum values in the data set.

$$Range = x_{max} - x_{min} = 15 = 15$$

The mean is calculated as the sum of all observations divided by the number of observations.

$$Mean = \frac{\sum_{i=1}^{N} x_i}{N} = \frac{64.1}{8} = 8$$

The variance is calculated as the average of the squared differences from the Mean.

$$Variance = \frac{\sum_{i=1}^{N} (x_i - Mean)^2}{N} = \frac{(2.8 - 8)^2 + (15 - 8)^2 + (5 - 8)^2 + (14 - 8)^2 + (7 - 8)^2 + (12 - 8)^2 + (8.3 - 8)^2 + (0 - 8)^2}{8} = 25.3$$

The standard deviation is the square root of the variance.

$$Standard Deviation = \sqrt{Variance} = \sqrt{25.3} = 5$$

Final Answer: