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Chapter 3: Q 3.78. (page 114)

Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation.

Router Horsepower. In the article "Router Roundup" T. Klenck reported on tests of seven fixed-base routers for perform features, and handling. The following table gives the horsepower for each of the seven routers tested .

1.75,2.25,2.25,2.25,1.75,2.00,1.50

Short Answer

Expert verified

Range of the data =0.75horse power

Standard deviation of the data=0.30horse power

Step by step solution

01

Step 1. Given information.  

We have given data:1.75,2.25,2.25,2.25,1.75,2.00,1.50

02

Step 2. To find range of the data.   

Range=Max.value-Min.value=2.25-1.50=0.75

03

Step 3. To find mean of the data. 

Mean=SumoftheobservationNumberofobservation=1.75+2.25+2.25+2.25+1.75+2.00+1.507=13.757=1.96429=1.96

04

Step 4. To find standard deviation of the data. 

x
x-x
x-x2
1.752.252.252.251.7521.5
-0.210.290.290.29-0.210.04-0.46
0.04410.08410.08410.08410.04410.00160.2116

Standardderivation=∑x-x2n-1=0.55376=0.30378=0.30hp

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Most popular questions from this chapter

Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences, The recommended dietary allowance (RDA) of iron for adult females under the age of 51is 18milligrams (mg) per day. The iron intakes during a 24-hour period for a random sample of45 adult females under the age of 51have a mean of 14.7mgand standard deviation of 3.1mg.

a. Construct a graph .
b. Apply Chebyshev's rule with k=2 to make pertinent statements about the observations in the sample.
c. Repeat part (b) with k=3.

Cuckoo Care. Many species of cuckoos are brood parasites. The females lay their eggs in the nests of smaller bird species, who then raise the young cuckoos at the expense of their own young. Data on the lengths, in millimeters (mm), of cuckoo eggs found in the nests of three bird species - the Tree Pipit. Hedge Sparrow, and Pied Wagtail - were collected by the late O.M. Latter in 1902and used by L.H.C. Tippett in his text The Methods of States (New York Wiley, 1952. p. 176). Use the following boxplots to compare the lengths of cuckoo eggs found in nests of the three bird species, paying special attention to center and variation.

What is another name for the Empirical rule? Why is that name appropriate?

Which measure of variation is preferred when

(a) the mean is used as a measure of center?

(b) the median is used as a measure of center?

Is an extreme observation necessary an outlier? Explain your answer.
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