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Chapter 1: Q52E (page 45)

The first four deviations from the mean in a sample of n=5 reaction times were .3, .9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for which these are the five deviations from the mean.

Short Answer

Expert verified

The fifth deviation from the mean is -3.5.

One of the samples is 5.3, 5.9, 6.0, 6.3, 1.5.

Step by step solution

01

Given information

The first four deviations from the mean were 0.3, 0.9, 1.0, 1.3.

The size of the sample is \(n = 5\).

02

Calculate the fifth deviation

Let x represents the fifth deviation.

We know that the sum of the deviations is 0.

Mathematically,

\(\begin{array}{c}0.3 + 0.9 + 1.0 + 1.3 + x &=& 0\\3.5 + x &=& 0\\x &=& - 3.5\end{array}\)

Thus, the fifth deviation is -3.5.

03

Obtain the sample of five observation

The sample observations are obtained as follows,

\({d_i} = {x_i} - \bar x \Rightarrow {{\bf{x}}_{\bf{i}}}{\bf{ = }}{{\bf{d}}_{\bf{i}}}{\bf{ + \bar x}}\)

Assuming the mean of the observations is 5\(\left( {\bar x} \right)\).\(\)

Thus, adding mean to each of the five deviations, the sample is given as,5.3, 5.9, 6.0, 6.3, 1.5.

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Most popular questions from this chapter

The article cited in Exercise 20 also gave the following values of the variables y=number of culs-de-sac and z=number of intersections:

y

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0

1

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2

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3

a. Construct a histogram for the ydata. What proportion of these subdivisions had no culs-de-sac? At least one cul-de-sac?

The three measures of center introduced in this chapter are the mean, median, and trimmed mean. Two additional measures of center that are occasionally used are the midrange,which is the average of the smallest and largest observations, and the midfourth,which is the average of the two fourths. Which of these five measures of center are resistant to the effects of outliers and which are not? Explain your reasoning.

Fire load (MJ/m2) is the heat energy that could bereleased per square meter of floor area by combustionof contents and the structure itself. The article 鈥淔ireLoads in Office Buildings鈥� (J. of Structural Engr.,

1997: 365鈥�368) gave the following cumulative percentages(read from a graph) for fire loads in a sample of388 rooms:

Value0 150 300 450 600

Cumulative %0 19.3 37.6 62.7 77.5

Value750 900 1050 1200 1350

Cumulative %87.2 93.8 95.7 98.6 99.1

Value1500 1650 1800 1950

Cumulative %99.5 99.6 99.8 100.0

a. Construct a relative frequency histogram and commenton interesting features.

b. What proportion of fire loads are less than 600? At least 1200?

c. What proportion of the loads are between 600 and1200?

The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. Would this be an enumerative or an analytic study? Explain yourreasoning.

Aortic stenosis refers to a narrowing of the aortic valve in the heart. The article 鈥淐orrelation Analysis of Stenotic Aortic Valve Flow Patterns Using PhaseContrast MRI鈥� (Annals of Biomed. Engr., 2005: 878鈥�887) gave the following data on aortic root diameter (cm) and gender for a sample of patients having various degrees of aortic stenosis:

M: 3.7 3.4 3.7 4.0 3.9 3.8 3.4 3.6 3.1 4.0 3.4 3.8 3.5
F: 3.8 2.6 3.2 3.0 4.3 3.5 3.1 3.1 3.2 3.0

  1. Compare and contrast the diameter observations for
    the two genders.
  2. Calculate a 10% trimmed mean for each of the two
    samples, and compare to other measures of center
    (for the male sample, the interpolation method men-
    tioned in Section 1.3 must be used).
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