In the entire population of a certain type of tree, the mean height of the trees is μ = 168.8 ft and the standard deviation is σ = 43.6 ft. You collect a random sample of n=22 trees. The distribution of these sample means is shown below. Each tick mark on the horizontal axis is a distance of one more standard error. Complete the indicated boxes, correct to two decimal places. mean of distribution=168.8 standard error=9.30   Note: The left box is 2 standard errors below the mean. The middle box is the mean. The right box is 2 standard errors above the mean.

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 + ...