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Chapter 3: Q. 3.104 (page 122)
What condition on a data set is required to apply the Empirical rule?
The condition which is required to apply Empirical rule is that data set should be with symmetric distribution.
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Objects such as asteroids and comets that come into proximity with the Earth are called near-Earth objects (NEOs). The National Aeronautics and Space Administration (NASA) tracks and catalogues all NEOs that are at least kilometer wide. Data on NEOs can be found on the NASA website; The following table gives the relative velocities in kilometers per second , arranged in increasing order, for the NEO close approaches to the earth during June .
The sample mean and sample standard deviation of these velocities are and 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 with
b. Repeat part (a) with
c. Interpret your results from parts (a) and (b).
Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.
a) Determine the mode of the data.
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer.
Medical School Faculty. The Association of American Medical College (AAMC) in a compiles data on medical school facility and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year.
Gestation Periods of Humans. Gestation periods of humans have a mean of days and a standard deviation of days. Let denote the variable "gestation period" for humans.
a. Find the standardized variable corresponding to
b. What are the mean and standard deviation of the standardized variable?
c. Obtain the -scores for gestation periods of days and days. Round your answers to two decimal places.
d. Interpret your answers in part (c).
c. Construct a graph similar to Fig. 3.20 on page 146 that shows your results from parts (b) and (c).
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.
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