The tallest living man at one time had a height of 

246246 

cm. The shortest living man at that time had a height of 

75.7

cm. Heights of men at that time had a mean of 

173.45 

cm and a standard deviation of 

7.06

cm. Which of these two men had the height that was more​ extreme?

To determine which man had a more extreme height relative to the population, we can use the concept of **z-scores**. The **z-score** measures how many standard deviations a data point is from the mean. The formula to calculate a z-score is:

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

Where:
- \(x\) is the individual data point (height in this case),
- \(\mu\) is the mean of the population,
- \(\sigma\) is the standard deviation of the population.

### For the tallest man:
- \(x = 246.246 \, \text{cm}\)
- \(\mu = 173.45 \, \text{cm}\)
- \(\sigma = 7.06 \, \text{cm}\)

\[
z_{\text{tall}} = \frac{246.246 - 173.45}{7.06}
\]

### For the shortest man:
- \(x = 75.7 \, \text{cm}\)
- \(\mu = 173.45 \, \text{cm}\)
- \(\sigma = 7.06 \, \text{cm}\)

\[
z_{\text{short}} = \frac{75.7 - 173.45}{7.06}
\]

Let's calculate these z-scores.The z-score for the tallest man is approximately **10.31**, and for the shortest man, it is approximately **-13.85**.

Since the magnitude of the z-score indicates how extreme the height is relative to the population:
- The shortest man has a more extreme height because his z-score of **-13.85** is further from zero compared to the tallest man's z-score of **10.31**.

Would you like a detailed explanation of the z-score concept or any other clarifications?

Here are 5 questions to expand this topic:
1. How can we interpret positive and negative z-scores in general?
2. How can extreme z-scores affect data analysis?
3. How is the z-score useful in determining outliers?
4. What are some applications of z-scores in real-world data?
5. Can z-scores help in comparing different data distributions?

**Tip:** Z-scores are highly useful for comparing data points from different distributions by standardizing them!

The tallest living man at one time had a height of 246.246 cm. The shortest living man at that time had a height of 75.7 cm. Heights of men at that time had a mean of 173.45 cm and a standard deviation of 7.06 cm. Which of these two men had the height that was more extreme?

Analyze the heights of the tallest and shortest living men using z-scores. Learn how to calculate z-scores for extreme values based on population statistics, including the mean of 173.45 cm and a standard deviation of 7.06 cm. Suitable for students in Grades 10-12.

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