One way to find the average temperature for a day is to take temperature readings at evenly spaced intervals for 24 hours and then find the average of those readings. A more sophisticated approach is to use Simpson’s rule and the formula for finding the average value of a function from Section 5.4. The temperature readings for 1 day are provided in this table:

a. Approximate the average temperature for this day by finding the numeric average of the temperature readings. Round all answers to 2 decimal places.

b. Approximate the average temperature using Simpson’s rule and the formula for finding the average value of a function. How do your answers compare? Which do you think is more representative of the average temperature? Explain.

c. Repeat parts (a) and (b), this time using only temperature readings taken every 6 hours starting at 12 A.M. Does this change your mind on which method you think is more effective?

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Time Temp (°F) 12 (A.M.) 2 4 6 8 10 12 (P.M.) 2 4 6 8 10 12 (A.M.) 81 81 79 75 70 68 64 61 60 71 74 78 65