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Chapter 3: Q 3.23. (page 101)

Find the

a. Mean b. median c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations.

Billionaires' Club. Each year, Forbes magazine compiles a list of the 400richest Americans. As of September 19,2012, the top 10 on the list are as shown in the following table.

Short Answer

Expert verified

a)$34.71billionsb)$29.45billionsc)$31.0billions

Step by step solution

01

Step 1. Given information. 

We have given data:66.0,46.0,41.0,31.0,31.0,27.9,26.8,26.3,26.1,25.0

02

Step 2. Mean of the data. 

Mean=SumofobservationNumberofobservation

=66.0+46.0+41.0+31.0+31.0+27.9+26.8+26.3+26.1+25.010=347.110=34.71

03

Step 3. Median of the data. 

Arrange the data in increasing order : 25.0,26.1,26.3,26.8,27.9,31.0,31.0,41.0,46.0,66.0

Median

localid="1651163731032" =5th+6th2=27.9+31.02=58.92=29.45

04

Step 4. Mode of the data. 

The greatest frequency is the mode of the data set.

The mode of the given data set is31.0

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Most popular questions from this chapter

The data set has 250observations and has mean 100and standard deviation 16. Approximately how many observations lie between 52and 148.

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 70modern Italian male skulls and that of 84preserved 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]

Consider the following sample of exam scores, arranged in increasing order.

The sample mean and sample standard deviation of these exam scores are 85and 16.1, respectively.
a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev's rule withk=2
b. Repeat part (a) with k=3
c. Interpret your results from parts (a) and (b).

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?

The data set has mean 30and standard deviation4 . Approximately what percentage of the observations lie between 22and 38?
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