The heights of women aged 20– 29 in the United States are approximately Normal with mean 64.2 inches and standard deviation 2.8 inches. The heights of men aged 20– 29 in the United States are approximately Normal with mean 69.4 inches and standard deviation 3.0 inches. What is the ?z‑score for a woman 5.5 feet tall? (Enter your answer rounded to two decimal places.) ?=     What is the z‑score for a man 5.5 feet tall? (Enter your answer rounded to two decimal places.) ?=z=     What information do the z‑scores give that the original non‑standardized heights do not? The z‑scores show us that the woman is slightly taller than average, while the man is much shorter than average. The z‑scores do not give us any additional information, since we already know that the man and woman have equal heights. The z‑scores show us that the woman is slightly shorter than average, while the man is much taller than average. The z‑scores show that the woman is slightly different from the average, while the man is very different from the average.

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 + ...