\( \begin{array}{lllllllllll}5.32 & 5.27 & 2.63 & 3.16 & 3.42 & 2.31 & 6.76 & 5.13 & 4.78 & 4.37 & 2.77 \\ 1.87\end{array} \) The range is 4.89 dollars. (Type an integer or decimal rounded to two decimal places as needed.) The variance is \( \square \) (Type an integer or decimal rounded to two decimal places as needed.)

To calculate the variance of the given dataset, follow these steps: ### **Dataset:** \[ 5.32, \, 5.27, \, 2.63, \, 3.16, \, 3.42, \, 2.31, \, 6.76, \, 5.13, \, 4.78, \, 4.37, \, 2.77, \, 1.87 \] ### **Step 1: Calculate the Mean** \[ \text{Mean} = \frac{\sum x_i}{n} = \frac{5.32 + 5.27 + 2.63 + 3.16 + 3.42 + 2.31 + 6.76 + 5.13 + 4.78 + 4.37 + 2.77 + 1.87}{12} = \frac{47.79}{12} = 3.98 \] ### **Step 2: Calculate Each Squared Deviation from the Mean** \[ \begin{align*} (5.32 - 3.98)^2 &= 1.34^2 = 1.79 \\ (5.27 - 3.98)^2 &= 1.29^2 = 1.66 \\ (2.63 - 3.98)^2 &= (-1.35)^2 = 1.83 \\ (3.16 - 3.98)^2 &= (-0.82)^2 = 0.68 \\ (3.42 - 3.98)^2 &= (-0.56)^2 = 0.32 \\ (2.31 - 3.98)^2 &= (-1.67)^2 = 2.80 \\ (6.76 - 3.98)^2 &= 2.78^2 = 7.71 \\ (5.13 - 3.98)^2 &= 1.15^2 = 1.32 \\ (4.78 - 3.98)^2 &= 0.80^2 = 0.64 \\ (4.37 - 3.98)^2 &= 0.39^2 = 0.15 \\ (2.77 - 3.98)^2 &= (-1.21)^2 = 1.47 \\ (1.87 - 3.98)^2 &= (-2.11)^2 = 4.46 \\ \end{align*} \] ### **Step 3: Sum All Squared Deviations** \[ \sum (x_i - \text{Mean})^2 = 1.79 + 1.66 + 1.83 + 0.68 + 0.32 + 2.80 + 7.71 + 1.32 + 0.64 + 0.15 + 1.47 + 4.46 = 24.82 \] ### **Step 4: Calculate the Variance** \[ \text{Variance} = \frac{\sum (x_i - \text{Mean})^2}{n} = \frac{24.82}{12} = 2.07 \] ### **Final Answer:** \[ \boxed{2.07} \]