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Chapter 3: Q. 19 (page 151)

Road Patrol. In the paper "Injuries and Risk Factors in a Vol. K. Reynolds et al. reported on a study commissioned by the U.S. Army. The purpose of the study was to improve medical planning and identify risk factors during multiple-day road patrols by examining the acute effects of long-distance marches by light-infantry soldiers. Each soldier carried a standard U.S. Army rucksack. Meal-Ready-to-Eat packages. and other field equipment. A sample of 10participating soldiers revealed the following data on total load mass, in kilograms.

a.Obtain the sample mean of these 10 load masses.
b.Obtain the range of the load masses.
c.Obtain the sample standard deviation of the load masses

Short Answer

Expert verified

Part(a) The sample mean is 45.7

Part(b) The range of load masses is 17

Part(c) The standard deviation is 4.09

Step by step solution

01

Part(a) Step 1: Given information

We are given a sample of participating soldiers with load mass.

02

Part(a) Step 2: Simplify

As we know mean of sample is sum of all data divided by total number of data. Therefore, the sample mean is

x=鈭�i=nxinx=48+50+45+49+44+47+37+54+40+4310=45.7

03

Part(b) Step 1: Given information

We are given a sample of participating soldiers with load mass.

04

Part(b) Step 2: Simplify

Range of sample is difference of highest value of data and lowest value of data.

Highest =54

Lowest =37

Range =54-37=17

05

Part(c) Step 1: Given information

We are given a sample of participating soldiers with load mass.

06

Part(c) Step 2: Simplify

Standard deviation of sample is given by

蟽=鈭�x2n-x2

Where,

x=mean of sample

n=Total number of sample

x=data in sample

Now,

鈭�x2n=482+502+452+492+442+472+372+542+402+43210鈭�x2n=2110.9x2=45.92=2106.81蟽=2110.9-2106.81=4.09

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Most popular questions from this chapter

Simple data sets have been given for you to try locating the descriptive metrics mentioned in this section. For each data set separately.

(a) Calculate the quartiles,

(b) calculate the interquartile range

(c)compile a five-number summary.

1,2,3,4,5,6,7,1,2,3,4,5,6,7

Regarding the interquartile range,

(a) What type of descriptive nature is it?

(b) What does it measure?

A quantitative data set has size 50. At least how many observations lie within three standard deviation to either side of the mean?

In this exercise, you will compare Chebyshev's rule and the empirical rule.

a. Compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. Comment on the differences.

b. Compare the estimates given by the two rules for the percentage of observations that lie within three standard deviations to either side of the mean. Comment on the differences.

The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, "The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones." In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O'Connor, cds., Littlc, Brown \& Co., 1959]
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