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Chapter 3: Q. 3.115 (page 122)
A quantitative data set has size . At least how many observations lie within three standard deviation to either side of the mean
observations lie within three standard deviation to either side of the mean.
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Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.
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?
Weekly Salaries. In the following table, we repeat the salary data in Data Set II from Example 3.1.
(a) Use Definitions 3.4 and 3.6 on pages 99 and 108, respectively, to obtain the sample mean and sample standard deviation of this (ungrouped) data set.
(b) A frequency distribution for Data Set II, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for thexf- values, that is, classmark or midpoint (which here is the same as the class) times class frequency. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean.
(c) Compare the answers that you obtained for the sample mean in parts (a) and (b). Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping. (Hint: What does xf represent for each class?)
(d) Construct a table similar to the one in part (b) but with columns for .Use the table and the grouped-data formula to obtain the sample standard deviation.
(e) Compare your answers for the sample standard deviation in parts (a) and (d). Explain why the grouped-data formula always yields the actual sample standard deviation when the data are grouped by using single-value grouping.
Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences, The recommended dietary allowance (RDA) of iron for adult females under the age of is milligrams (mg) per day. The iron intakes during a -hour period for a random sample of adult females under the age of have a mean of and standard deviation of .
a. Construct a graph .
b. Apply Chebyshev's rule with to make pertinent statements about the observations in the sample.
c. Repeat part (b) with .
Dallas Mavericks. From the ESPN website, in the Dallas Mavericks Roster, we obtained the following ages, in years, for the players on that basketball team for the season.
Obtain the following parameters for these ages. Use the appropriate mathematical notation for the parameters to express your answers.
a. Mean
b. Standard deviation
c. Median
d. Mode
e. IQR
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