To find the IQR (Interquartile Range) from the given information: Minimum = 15 min, Q1 = 27 min (25th percentile), Q2 = 31 min (median), Q3 = 32 min (75th percentile), Maximum = 50 min. The IQR calculation is IQR = Q3 - Q1 = 32 - 27 = 5. For identifying outliers, apply the k = 1.5 rule. The expected range is [Q1 - 1.5*IQR, Q3 + 1.5*IQR] = [27 - 1.5*5, 32 + 1.5*5] = [19.5, 39.5]. The actual range is [15, 50]. The minimum value is below 19.5, and the maximum value exceeds 39.5. Hence, outliers are present. Conclusion: Outliers exist.
B. quadratic. To determine whether a function is linear, quadratic, or exponential without graphing, examine the first, second, and third differences between the terms. If the first differences remain constant, the function is linear; if the second differences are constant, it is quadratic; if the third differences are constant, it is cubic. If the fourth differences do not remain constant, the function may be exponential. Here, the first differences are not constant, ruling out linearity. However, the second differences are constant (around $0.18 each), indicating a quadratic function. The accompanying graph supports that the points closely align with a quadratic model.
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