Exam 2: Describing the Distribution of a Single Variable
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Suppose that an analysis of a set of test scores reveals that:
, and
-What can you say about the relative position of each of the observations 34, 84, and 104?



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The data shown below contains family incomes (in thousands of dollars) for a set of 50 families sampled in 2007 and 2017. Assume that these families are good representatives of the entire United States.
-Find the mean, median, standard deviation, first and third quartiles, and the 95th percentile for family incomes in both years.

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The number of car insurance policy holders is an example of a discrete numerical variable.
(True/False)
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The interquartile range (IQR) encompasses what percent of the observations?
(Multiple Choice)
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A distribution with a high kurtosis has almost all of its observations within three standard deviations of the mean.
(True/False)
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A frequency table indicates how many observations fall within each category, and a histogram is its graphical analog.
(True/False)
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Data that arise from counts are best described as _____ data.
(Multiple Choice)
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There are four quartiles that divide the values in a data set into four equal parts.
(True/False)
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What measure of distribution relates to extreme events, such as a stock market crash?
(Multiple Choice)
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As a graphical tool, the histogram is ideal for showing whether the distribution of a numerical variable is symmetric or skewed.
(True/False)
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A think tank of economists is interested in how the distribution of family income has changed in Country X during the last 20 years. The summary measures and histograms shown below are generated for a sample of 500 family incomes, using the 1997 and 2017 income for each family in the sample.
Summary Measures (in thousands of dollars):
Based on these results, discuss as completely as possible how the distribution of family income in Country X changed from 1997 to 2017.



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The median of a data set with 30 values would be the average of the 15th and the 16th values when the data values are arranged in ascending order.
(True/False)
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In order for the characteristics of a sample to be generalized to the entire population, the sample should be:
(Multiple Choice)
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Based on the histogram shown below, how would you describe the age distribution for these data? 

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