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Chapter 3: Q. 3.156 (page 136)
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?
(a) The standard deviation is used as a measure of variation.
(b) The interquartile range is used as a measure of variation.
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Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.
Fill in the following blanks.
(a) A standardized variable always has mean _____ and standard deviation _______ .
(b) The z-score corresponding to an observed value of a variable tells you ______ .
(c) A positive z-score indicates that the observation is ______ the mean, whereas a negative z-score indicates that the observation is _______ the mean.
The data set has size. Approximately how many observations lie within three standard deviations to either side of the mean?
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
Outliers and trimmed means. Some data sets contain outliers, observation that fall well outside the overall pattern of the data(We discuss outliers in more detail in section 3.4) Suppose, for instance that you are interested in the ability o high school algebra student to compute square roots. You decide to give a square root exam to 10 of these students Unfortunately, one of the student had a fight with his girlfriend and cannot concentrate he gets a 0. The 10 score are displayed in increasing order in the following table. The score of 0 is an outlier.
Statisticians have a systematic method for avoiding extreme observation and outliers when they calculated means. They compute trimmed means, in which high and low observation are deleted or "trimmed off" before the mean is calculated . For instance, to compute the 10% trimmed mean of the test score data. we first delete both the bottom 10% and the top 10% of the ordered data. that is,0 and 80. Then we calculated the mean of the remaining data. Thus the10% trimmed mean of the test score data is
The following table displays a set of score for a 40 question algebra final
Part (a) Do any the score look like outliers?
Part (b) Compute the usual mean of the data.
Part (c) Compute the 5% trimmed mean of the data.
Part (d) Compute the 10% trimmed mean of the data.
Part (e) Compare the means you obtained in parts (b) (d) which of the three provides the best measure of center for the data?
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