Bigfoot Field Researchers Organization maintains a database of bigfoot/sasquatch sightings and related reports. According to the BFRO database as of December 2020 the mean number of reports per county in the state of Illinois is 2.92 (standard deviation = 4.02). Here are the z-scores for a few specific counties: Carroll County: z = -0.72 Du Page County: z = +0.27 Cook County: z = +3.26 a. Which of these three counties is most representative of the typical county in Illinois in terms of the number of bigfoot reports? Why? b. How many reports have there been in Cook County? (round to a number that makes sense; Don’t forget to state the equation)

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 + ...