Question

The tallest living man at one time had a height of 265 cm. The shortest living man at that time had a height of 109.1 cm. Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm. Which of these two men had the height that was more​ extreme?

Answer 1

Answer:

tallest man height is more extreme.

Step-by-step explanation:

Given:

Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.

Concept used:

Convert height into z scores for comparison of deviation from the mean.

Solution:

Tallest man height = 265 cm

$Z_{tall} =\frac{265-173.73}{8.65} \\=10.55$

Shortest man height = 109.1 cm

$Z_{short} =\frac{109.1-173.73}{8.65} \\=-7.47$

Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.

Hence tallest man height is more extreme.

Answer 2

The tallest man has the more extreme height.

The person with the more extreme height is the one that is furthest from the mean.

The difference between the mean height and the tallest man is:

= 265 - 173.73

= 91.27 cm

The difference between the mean height and the shortest man is:

= 173.73 - 109.1

= 64.63 cm

The tallest man is therefore more extreme because he is farthest from the mean.

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