\begin{tabular}{lllllllllll}5.32 & 5.27 & 2.63 & 3.16 & 3.42 & 2.31 & 6.76 & 5.13 & 4.78 & 4.37 & 2.77 \\ \hline\end{tabular} The range is 4.89 (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, we first need to find the mean (average) of the data set. The numbers provided are: 5.32, 5.27, 2.63, 3.16, 3.42, 2.31, 6.76, 5.13, 4.78, 4.37, 2.77. Let's calculate the mean: Mean = (5.32 + 5.27 + 2.63 + 3.16 + 3.42 + 2.31 + 6.76 + 5.13 + 4.78 + 4.37 + 2.77) / 11 Mean = (46.01) / 11 Mean ≈ 4.18 (rounded to two decimal places). Next, we'll calculate the variance using the formula: Variance \( \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} \) Where \( x_i \) is each number in the dataset, \( \mu \) is the mean, and \( N \) is the number of observations. Calculating each deviation squared: - (5.32 - 4.18)² = (1.14)² ≈ 1.2996 - (5.27 - 4.18)² = (1.09)² ≈ 1.1881 - (2.63 - 4.18)² = (-1.55)² ≈ 2.4025 - (3.16 - 4.18)² = (-1.02)² ≈ 1.0404 - (3.42 - 4.18)² = (-0.76)² ≈ 0.5776 - (2.31 - 4.18)² = (-1.87)² ≈ 3.4969 - (6.76 - 4.18)² = (2.58)² ≈ 6.6564 - (5.13 - 4.18)² = (0.95)² ≈ 0.9025 - (4.78 - 4.18)² = (0.60)² ≈ 0.3600 - (4.37 - 4.18)² = (0.19)² ≈ 0.0361 - (2.77 - 4.18)² = (-1.41)² ≈ 1.9881 Now, summing these squared deviations: Total ≈ 1.2996 + 1.1881 + 2.4025 + 1.0404 + 0.5776 + 3.4969 + 6.6564 + 0.9025 + 0.3600 + 0.0361 + 1.9881 ≈ 19.4897 Now, we divide by the number of observations (N = 11): Variance ≈ 19.4897 / 11 ≈ 1.7727 Therefore, the variance rounded to two decimal places is approximately **1.77**.