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4.4 Heights of adults: Researchers studying anthropometry collected body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender, for 507 physically active individuals. The histogram below shows the sample distribution of heights in centimeters (Heinz, 2003).

Min	147.2
Q1	163.8
Median	170.3
Mean	171.1
SD	9.4
Q3	177.8
Max	198.1

a) What is the point estimate for the average height of active individuals? cm
b) What is the median height of these active individuals? cm
c) What is the point estimate for the standard deviation of the heights of active individuals? cm
d) The IQR extends from cm to cm, giving an IQR of cm.
e) Is a person who is 1m 80cm (180cm) tall considered unusually tall? And is a person who is 1m 55cm (155cm) considered unusually short?

Yes, they are unusual since these heights are more than two standard deviations away from the mean
No, they are not unusual since these heights are within two standard deviations of the mean
No people can come in all sizes, we cannot define usual or unusual heights
We cannot tell from the given information

f) The researchers take another random sample of physically active individuals. Would you expect the mean and standard deviation of the new sample to be the ones given above?

No, the mean and standard deviation would not be the same, but should be close to those given above
The mean and standard deviation from a new sample are likely to be drastically different from those given above
Yes, the mean and standard deviation do not change just because of who we sampled

g) The sample means obtained are point estimates for the mean height of all active individuals, if the sample of individuals is equivalent to a simple random sample. What measure do we use to quantify the variability of such and estimate (Hint: recall that $\displaystyle {S}{D}_{{x}}={\frac{{\sigma}}{{\sqrt{{{n}}}}}}$ )?
Compute this quantity using the data from the original sample under the condition that the data are from a simple random sample.
$\displaystyle {S}{D}_{{x}}={\frac{{\sigma}}{{\sqrt{{{n}}}}}}$ = (please round to four decimal places)

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