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Chapter 3: Q. 6 (page 151)

Data Set A has more variation than Data Set B. Decide which of the following statements are necessarily true.

a. Data Set A has a larger mean than Data Set B.

b. Data Set A has a larger standard deviation than Data Set B.

Short Answer

Expert verified

a. False

b. True

Step by step solution

01

Part a.

Given statement is false because mean is independent of variation of data and depends only on sum of observations.

02

Part b.

The given assertion is correct. The standard deviation is a measure of variance that shows how much the observations deviate from the mean on average. The standard deviation will be considered for a data collection with a lot of variances since the observations will be distant from the mean on average. The standard deviation will be minimal for a data collection with a small degree of variance since the observations will be near to the mean on average.

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Most popular questions from this chapter

In each Exercises 3.82-3.90, use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don't apply, explain why. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

U.S. Hospitals. The American Hospital Association conducts annual surveys of hospitals in the United States and publishes its findings in AHA Hospital Statistics. Data on hospital type for U.S. registered hospitals can be found on the WeissStats site. For convenience, we use the following abbreviations:

  • NPC: Nongovernment not-for-profit community hospitals
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Consider the data set 3,3,3,3,3,3.

Part (a) Guess the value of the sample standard deviation without calculating it. Explain your reasoning

Part (b) Use the defining formula to calculate the sample standard deviation.

Part (c) Complete the following statement and explain your reasoning. If all observation in a data set are equal, the sample standard deviation is

Part (d) Complete the following statement and explain your reasoning. If the sample standard deviation of a data set is 0 then...

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A company produces cans of stewed tomatoes with an advertised weight of 14oz. The standard deviation of the weights is known to be 0.4oz. A quality - control engineer selects a can of stewed tomatoes at random and finds its net weight to be 17.28oz.

Part (a): Estimate the relative standing of that can of stewed tomatoes, assuming the true mean weight is 14oz. Use the z-score and Chebyshev's rule.

Part (b): Does the quality - control engineer have reason to suspect that the true mean weight of all cans of stewed tomatoes being produced is not 14oz? Explain your answer.

Specify the mathematical symbol used for each of the following descriptive measures. a. Sample mean b. Sample standard deviation c. Population mean d. Population standard deviation.
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