Forest Fires in Portugal A study of forest fires in Portugal looked at the effect of many variables on the area of forest that is burned by the fire. The study included 517 forest fires and found a mean area burned of 12.85 hectares with a standard deviation of 63.66. (The standard deviation is much bigger than the mean because the data is very right-skewed.) Find and interpret a 90% confidence interval for the mean area burned by all forest fires in Portugal. A) What is the Confidence interval (round to three decimal places): B) Interpretation: A. We are confident that 90% of the forest fires in this sample burn an area within those two numbers. B. We are 90% confident that the mean area burned for all forest fires in Portugal is between those two numbers. C. We are confident that 90% of forest fires in Portugal burn an area within those two numbers. D. We are 90% confident that the mean area burned for this sample of forest fires in Portugal is between those two numbers.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...