Use $z$ scores to compare the given values. The tallest living man at one time had a height of $231 \mathrm{~cm}$. The shortest living man at that time had a height of $120.1 \mathrm{~cm}$. Heights of men at that time had a mean of $170.89 \mathrm{~cm}$ and a standard deviation of $6.85 \mathrm{~cm}$. Which of these two men had the height that was more extreme? Since the $z$ score for the tallest man is $z=$ and the $z$ score for the shortest man is $z=$ the man had the height that was more extreme. (Round to two [ecimal places.)

Step 1 ：Given that the tallest living man at one time had a height of 231 cm, the shortest living man at that time had a height of 120.1 cm, the mean height of men at that time was 170.89 cm, and the standard deviation was 6.85 cm.

Step 2 ：We need to find out which of these two men had the height that was more extreme. To do this, we will calculate the z-scores for both the tallest and shortest man and compare them. The man with the higher absolute z-score has the more extreme height.

Step 3 ：The z-score is a measure of how many standard deviations an element is from the mean. It is calculated using the formula \(z = \frac{x - \mu}{\sigma}\), where \(x\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 4 ：First, calculate the z-score for the tallest man: \(z = \frac{231 - 170.89}{6.85} = 8.78\).

Step 5 ：Next, calculate the z-score for the shortest man: \(z = \frac{120.1 - 170.89}{6.85} = -7.41\).

Step 6 ：Compare the absolute values of the z-scores. The absolute value of 8.78 is greater than the absolute value of -7.41.

Step 7 ：\(\boxed{\text{Therefore, the tallest man had the height that was more extreme.}}\)