4.4) Researchers studying anthropometry collected body girth measurements and sk
ID: 3218643 • Letter: 4
Question
4.4) 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 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 an estimate? Compute this quantity using the data from the original sample under the condition that the data are a simple random sample.
100 80 60 40 20 150 160 170 Height 180 190 200 Min 147.2 163.8 Q1 Median 170.3 Mean 171.1 SD 9.4 Q3 198.1 MaxExplanation / Answer
(a) Point estimate of the average height is given by sample mean, which is given as 171.1
The median is estimated by sample median, which is given as 170.3
(b) For std dev, estimate is: sample stdev = 9.4 .
Estimate for IQR wil be sample IQR
= Q3 - Q1
= 177.8 - 163.8
= 14
(c) Both statements are right, since 1.80 is beyond Q3 and 1.55 is below Q1. Hence, person with 1.8 has at least 75% people smaller than him and that with 1.55 has at least 75% people taller than him.
(d) No. Different sample have different values. So, in precise terms, mean and std dev will be certainly different. However, as sample size is of a large number 507, it is liekly that these values won't change much in the new sample.
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