Researchers studying anthropometry collected body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender, for 507 physically active individuals. Use the table to answer the questions.Min147.2Q1164.3Median171.3Mean172.5SD8.7Q3178.1Max198.1 a) What is the point estimate for the average height of active individuals? ______________ cmb) What is the median height of these active individuals? ______________ cmc) What is the point estimate for standard deviation of heights of active individuals? ____________ cmd) The IQR extends from ______________ cm to ______________ cm, giving an IQR of ______________ cm.e) Is a person who is 1m 90cm (190cm) tall considered unusually tall? And is a person who is 1m 50cm (150cm) considered unusually short?__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__Yes, they are unusual since these heights are more than two standard deviations away from the mean__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?__The mean and standard deviation from a new sample are likely to be drastically different from those given above__No, the mean and standard deviation would not be the same, but should be close to 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 an estimate (Hint: recall that )?Compute this quantity using the data from the original sample under the condition that the data are from a simple random sample. = __________________ (please round to four decimal places)

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Answered: Researchers studying anthropometry…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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. Use the table to answer the questions.

Min	147.2
Q1	164.3
Median	171.3
Mean	172.5
SD	8.7
Q3	178.1
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 standard deviation of 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 90cm (190cm) tall considered unusually tall? And is a person who is 1m 50cm (150cm) considered unusually short?
__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
__Yes, they are unusual since these heights are more than two standard deviations away from the mean
__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?
__The mean and standard deviation from a new sample are likely to be drastically different from those given above
__No, the mean and standard deviation would not be the same, but should be close to 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 an estimate (Hint: recall that )?

Compute this quantity using the data from the original sample under the condition that the data are from a simple random sample.

= __________________ (please round to four decimal places)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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