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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

Augusta National Golf Course. Earlier in this section, we found that the population standard deviation of the lengths of the holes at the Augusta National Golf Club is 132.0yd. In this context. is the number 132.0a parameter or a statistic? Explain your answer.

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.

A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6掳FThe results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of 98.6掳Fthe Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" (Journal of the American Medical Association ). Among other data, the researchers obtained the body temperatures of 93healthy humans. The temperatures had a mean of 98.1掳Fand a standard deviation of 0.65掳F

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

Identify a use of lower and upper limits.

Identify each quantity as a parameter or a static

(a) 渭

(b) s

(c) x炉

(d)蟽
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