BUSINESS ANALYTICS FINAL EXAM QUESTIONS AND
VERIFIED ANSWERS
Histogram - Answers - a graph for a quantitative variable; we usually slice up all the
possible values into bins and then count the number of cases that fall in each bin
Relative frequency histograms - Answers - percentages of each bin in the histogram
Stem-and-leaf displays - Answers - are like histograms, but they also give the individual
values
Quantitative Data Condition - Answers - Before making a histogram or stem-and-leaf
display; the data must be values of a quantitative variable whose units are known
When describing a distribution, attention should be paid to - Answers - its shape, center,
spread
Shape - Answers - a distribution in terms of its modes, its symmetry, and whether it has
any gaps or outlying values
Modes - Answers - Peaks or humps seen in a histogram
Unimodal - Answers - A distribution whose histogram has one main peak
Bimodal - Answers - Two main peaks
Multimodal - Answers - three or more peaks
Uniform - Answers - A distribution whose histogram doesn't appear to have any mode
and in which all the bars are approximately the same height
Symmetric - Answers - the halves on either side of the center look, at least
approximately, like mirror images
Tails - Answers - The thinner ends of a distribution
Skewed - Answers - If one tail stretches out farther than the other: skewed to side of
where tail is
Judgment call - Answers - Characterizing the shape of a distribution
The mean is a natural summary for - Answers - unimodal, symmetric distributions
,Mean - Answers - sum of y values (or x values)/ number of variables
If a distribution is skewed, contains gaps, or contains outliers, then it is better to use -
Answers - the median
The median is - Answers - resistant
Range - Answers - max-min; not resistant to unusual observations
quartiles - Answers - values that frame the middle 50% of the data. One quarter of the
data lies below the lower quartile, Q1, and one quarter lies above the upper quartile, Q3
The interquartile range (IQR) - Answers - defined to be the difference between the two
quartile values; Q3-Q1
Standard deviation - Answers - takes into account how far each value is from the mean;
appropriate for symmetric distributions; square root of the variance
Variance - Answers - (s^2) average of the squared deviations; sum of (y value minus
the mean)^2 / n-1
If the shape is skewed - Answers - the median and IQR should be reported
If the shape is unimodal and symmetric - Answers - the mean and standard deviation
and possibly the median and IQR should be reported
Always pair the median with - Answers - IQR
Always pair the mean with - Answers - standard deviation
Z-score - Answers - the standardized value tells how many standard deviations each
value is above or below the overall mean; x minus the mean/ standard deviation
The five-number summary of a distribution - Answers - reports its median, quartiles, and
extremes (maximum and minimum)
Boxplot - Answers - highlights several features of the distribution of the variable,
including the quartiles, the median, and any outlying values
Time series plot - Answers - A display of values against time
Smooth trace - Answers - To better understanding the trend of times series data
Stationary - Answers - when a time series is without a strong trend or change in
variability
, Scatterplot - Answers - plots one quantitative variable against another, is an effective
display to look for trends, patterns, and relationships between two quantitative variables
Negative pattern - Answers - A pattern that runs from the upper left to the lower right
Positive pattern - Answers - A pattern running from the lower left to the upper right
Linear - Answers - If there is a straight-line relationship, it will appear as a cloud or
swarm of points stretched out in a generally consistent, straight form
Form - Answers - straight, curved, exotic
Strength - Answers - how much scatter or cluster
Outlier - Answers - unusual observation, standing away from the overall pattern of the
scatterplot
We place the explanatory or predictor variable on - Answers - the x-axis
We place the response variable on - Answers - the y-axis
The x- and y-variables are sometimes referred to as - Answers - the independent and
dependent variables
x variable - Answers - independant
y variable - Answers - dependant
Correlation coefficient - Answers - Since x's and y's are paired, multiply each
standardized value of x by the standardized value it is paired with and add up those
cross products. Divide by n -1.The ratio of the sum of the product zxzy for every point in
the scatterplot to n - 1
Correlation - Answers - measures the strength of the linear association between two
quantitative variables
Before using correlation, you must check - Answers - Quantitative Variable Condition
Linearity Condition
Outlier Condition
Quantitative Variables Condition - Answers - Correlation applies only to quantitative
variables
Linearity Condition - Answers - Correlation measures the strength only of the linear
association. If the underlying relationship is curved, summarizing its strength with a
correlation would be misleading.
VERIFIED ANSWERS
Histogram - Answers - a graph for a quantitative variable; we usually slice up all the
possible values into bins and then count the number of cases that fall in each bin
Relative frequency histograms - Answers - percentages of each bin in the histogram
Stem-and-leaf displays - Answers - are like histograms, but they also give the individual
values
Quantitative Data Condition - Answers - Before making a histogram or stem-and-leaf
display; the data must be values of a quantitative variable whose units are known
When describing a distribution, attention should be paid to - Answers - its shape, center,
spread
Shape - Answers - a distribution in terms of its modes, its symmetry, and whether it has
any gaps or outlying values
Modes - Answers - Peaks or humps seen in a histogram
Unimodal - Answers - A distribution whose histogram has one main peak
Bimodal - Answers - Two main peaks
Multimodal - Answers - three or more peaks
Uniform - Answers - A distribution whose histogram doesn't appear to have any mode
and in which all the bars are approximately the same height
Symmetric - Answers - the halves on either side of the center look, at least
approximately, like mirror images
Tails - Answers - The thinner ends of a distribution
Skewed - Answers - If one tail stretches out farther than the other: skewed to side of
where tail is
Judgment call - Answers - Characterizing the shape of a distribution
The mean is a natural summary for - Answers - unimodal, symmetric distributions
,Mean - Answers - sum of y values (or x values)/ number of variables
If a distribution is skewed, contains gaps, or contains outliers, then it is better to use -
Answers - the median
The median is - Answers - resistant
Range - Answers - max-min; not resistant to unusual observations
quartiles - Answers - values that frame the middle 50% of the data. One quarter of the
data lies below the lower quartile, Q1, and one quarter lies above the upper quartile, Q3
The interquartile range (IQR) - Answers - defined to be the difference between the two
quartile values; Q3-Q1
Standard deviation - Answers - takes into account how far each value is from the mean;
appropriate for symmetric distributions; square root of the variance
Variance - Answers - (s^2) average of the squared deviations; sum of (y value minus
the mean)^2 / n-1
If the shape is skewed - Answers - the median and IQR should be reported
If the shape is unimodal and symmetric - Answers - the mean and standard deviation
and possibly the median and IQR should be reported
Always pair the median with - Answers - IQR
Always pair the mean with - Answers - standard deviation
Z-score - Answers - the standardized value tells how many standard deviations each
value is above or below the overall mean; x minus the mean/ standard deviation
The five-number summary of a distribution - Answers - reports its median, quartiles, and
extremes (maximum and minimum)
Boxplot - Answers - highlights several features of the distribution of the variable,
including the quartiles, the median, and any outlying values
Time series plot - Answers - A display of values against time
Smooth trace - Answers - To better understanding the trend of times series data
Stationary - Answers - when a time series is without a strong trend or change in
variability
, Scatterplot - Answers - plots one quantitative variable against another, is an effective
display to look for trends, patterns, and relationships between two quantitative variables
Negative pattern - Answers - A pattern that runs from the upper left to the lower right
Positive pattern - Answers - A pattern running from the lower left to the upper right
Linear - Answers - If there is a straight-line relationship, it will appear as a cloud or
swarm of points stretched out in a generally consistent, straight form
Form - Answers - straight, curved, exotic
Strength - Answers - how much scatter or cluster
Outlier - Answers - unusual observation, standing away from the overall pattern of the
scatterplot
We place the explanatory or predictor variable on - Answers - the x-axis
We place the response variable on - Answers - the y-axis
The x- and y-variables are sometimes referred to as - Answers - the independent and
dependent variables
x variable - Answers - independant
y variable - Answers - dependant
Correlation coefficient - Answers - Since x's and y's are paired, multiply each
standardized value of x by the standardized value it is paired with and add up those
cross products. Divide by n -1.The ratio of the sum of the product zxzy for every point in
the scatterplot to n - 1
Correlation - Answers - measures the strength of the linear association between two
quantitative variables
Before using correlation, you must check - Answers - Quantitative Variable Condition
Linearity Condition
Outlier Condition
Quantitative Variables Condition - Answers - Correlation applies only to quantitative
variables
Linearity Condition - Answers - Correlation measures the strength only of the linear
association. If the underlying relationship is curved, summarizing its strength with a
correlation would be misleading.
