esearchers 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

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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(a) What is the point estimate for the average height of active individuals? What about the  median?

(b) What is the point estimate for the standard deviation of the heights of active individuals?

What about the IQR?

(c) Is a person who is 1m 80cm (180 cm) tall considered unusually tall? And is a person who is  1m 55cm (155cm) considered unusually short? Explain your reasoning.

(d) The researchers take another random sample of physically active individuals. Would you

expect the mean and the standard deviation of this new sample to be the ones given above.

Explain your reasoning.

(e) The samples 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 an estimate? Compute this quantity using the data from  the original sample under the condition that the data are a simple random sample

Step-by-step explanation:

1. the point estimate for the average height is the mean = 171.1

the median of active individuals is 170.3

2. point estimate of sd = 9.4

to get IQR

= 177.8 -163.8

= 14

3. mean +- SD

171.1 +-2(9.4)

171.1+18.8  = 189.9

171.1-18.8 = 152.3

[189.9, 152.3]

180CM is within the limits of 2SD. so a height of 180cm is not unusually tall

155 cm is within the 2sd limit so this height is not unusually short

4.

mean and sd are not same. a great probability exists that a different sample would have similar but different results if the same sample size is 507.

5.

= 0.417

≈ 0.42