The tallest living man at one time had a height of 240 cm. The shortest living man at that time had a height of 85.9 cm. Heights of men at that time had a mean of 171.42 cm and a standard deviation of 6.51 cm. Which of these two men had the height that was more​ extreme? round to two decimals

To determine which of the two men had a more extreme height, we need to calculate their respective **z-scores**. The z-score measures how many standard deviations a value is from the mean. The formula for the z-score is:

\[
z = \frac{x - \mu}{\sigma}
\]

Where:
- \( x \) is the height of the person,
- \( \mu \) is the mean height,
- \( \sigma \) is the standard deviation.

### For the tallest man:
- \( x = 240 \, \text{cm} \)
- \( \mu = 171.42 \, \text{cm} \)
- \( \sigma = 6.51 \, \text{cm} \)

\[
z_{\text{tallest}} = \frac{240 - 171.42}{6.51}
\]

### For the shortest man:
- \( x = 85.9 \, \text{cm} \)
- \( \mu = 171.42 \, \text{cm} \)
- \( \sigma = 6.51 \, \text{cm} \)

\[
z_{\text{shortest}} = \frac{85.9 - 171.42}{6.51}
\]

Let me calculate these z-scores.The z-score for the tallest man is \( 10.53 \), and for the shortest man, it is \( -13.14 \). Since the magnitude of the shortest man's z-score is larger (ignoring the sign), his height is more extreme compared to the population mean.

Would you like more details or have any questions?

Here are 5 related questions:
1. What does a z-score represent in statistics?
2. How do extreme z-scores affect data interpretation?
3. What is considered an outlier based on z-scores?
4. Can the standard deviation of a dataset change over time?
5. How would you calculate the height percentile for these men?

**Tip**: A z-score with a high absolute value indicates that the data point is far from the mean and may be considered an outlier.

This problem compares the heights of the tallest and shortest living men with a statistical approach using z-scores. Learn how to determine which height is more extreme relative to the population mean of 171.42 cm, with a standard deviation of 6.51 cm. Suitable for students in Grades 9-12.

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