QUANTITATIVE REASONING EXAM QUESTIONS WITH 100%
VERIFIED ANSWERS
If X is correlated with Y, what must be true about X and Y? Explain your
reasoning. - ANSWER Increasing values of X go with either increasing or
decreasing values of Y. A correlation exists between X and Y when higher values
of X consistently go with higher values of Y or when higher values of X
consistently go with lower values of Y.
- - ANSWER Evidence that higher rates of defects are correlated with exposure to
greater amounts of smoke. If higher rates of defects are correlated with exposure to
greater amounts of smoke, it is more likely that second-hand smoke is a cause of
birth defects.
Suppose you are given the mean and just one data value from a distribution. What
can you calculate? - ANSWER The deviation for the single value can be calculated,
because it depends only on that value and the mean.
Which data set would you expect to have the highest standard deviation: heights
(lengths) of newborn infants, heights of all elementary-school children, or heights
of first-grade boys? - ANSWER The heights of all elementary-school children,
since it has the largest range.
Describe how the range of a distribution is defined and calculated. - ANSWER The
range of a data set is the difference between its highest and lowest data values.
Define the five-number summary, and explain how to depict it visually with a
boxplot. - ANSWER - low value, lower quartile, median, upper quartile, and high
value
- Draw a number line that spans all the values in the data set. Enclose the values
from the lower to upper quartile in a box. Draw a vertical line through the box at
the median. Add "whiskers" extending to the low and high values.
Briefly describe the use of the range rule of thumb for interpreting the standard
deviation. What are its limitations? - ANSWER The standard deviation is
approximately the range divided by four. The range rule of thumb does not work
, well when the highest or lowest value is an outlier.
The highest exam score was in the upper quartile of the distribution. - ANSWER
The statement makes sense because the highest score will be in the highest quartile.
Decide whether the following statement makes sense (or is clearly true) or does not
make sense (or is clearly false). Explain your reasoning.
I examined the data carefully, and the range was greater than the standard
deviation. - ANSWER The statement makes sense because the range is
approximately four times the standard deviation.
The mean gas mileage of the compact cars we tested was 34 miles per gallon, with
a standard deviation of 5 gallons. - ANSWER The statement does not make sense
because the standard deviation should have the same units as the mean and the data.
Find the mean and median for the waiting times at Big Bank given below. Show
your work clearly, and verify that both are the same. The following values are
measured in minutes.
Big Bank (three lines): 4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0 - ANSWER
mean= sum of all values/total number value
sum: 79.2
number of values: 11
mean: 7.2
median: 6th
7.2
equal
After recording the pizza delivery times for two different pizza shops, you conclude
that one pizza shop has a mean delivery time of
44
minutes with a standard deviation of
VERIFIED ANSWERS
If X is correlated with Y, what must be true about X and Y? Explain your
reasoning. - ANSWER Increasing values of X go with either increasing or
decreasing values of Y. A correlation exists between X and Y when higher values
of X consistently go with higher values of Y or when higher values of X
consistently go with lower values of Y.
- - ANSWER Evidence that higher rates of defects are correlated with exposure to
greater amounts of smoke. If higher rates of defects are correlated with exposure to
greater amounts of smoke, it is more likely that second-hand smoke is a cause of
birth defects.
Suppose you are given the mean and just one data value from a distribution. What
can you calculate? - ANSWER The deviation for the single value can be calculated,
because it depends only on that value and the mean.
Which data set would you expect to have the highest standard deviation: heights
(lengths) of newborn infants, heights of all elementary-school children, or heights
of first-grade boys? - ANSWER The heights of all elementary-school children,
since it has the largest range.
Describe how the range of a distribution is defined and calculated. - ANSWER The
range of a data set is the difference between its highest and lowest data values.
Define the five-number summary, and explain how to depict it visually with a
boxplot. - ANSWER - low value, lower quartile, median, upper quartile, and high
value
- Draw a number line that spans all the values in the data set. Enclose the values
from the lower to upper quartile in a box. Draw a vertical line through the box at
the median. Add "whiskers" extending to the low and high values.
Briefly describe the use of the range rule of thumb for interpreting the standard
deviation. What are its limitations? - ANSWER The standard deviation is
approximately the range divided by four. The range rule of thumb does not work
, well when the highest or lowest value is an outlier.
The highest exam score was in the upper quartile of the distribution. - ANSWER
The statement makes sense because the highest score will be in the highest quartile.
Decide whether the following statement makes sense (or is clearly true) or does not
make sense (or is clearly false). Explain your reasoning.
I examined the data carefully, and the range was greater than the standard
deviation. - ANSWER The statement makes sense because the range is
approximately four times the standard deviation.
The mean gas mileage of the compact cars we tested was 34 miles per gallon, with
a standard deviation of 5 gallons. - ANSWER The statement does not make sense
because the standard deviation should have the same units as the mean and the data.
Find the mean and median for the waiting times at Big Bank given below. Show
your work clearly, and verify that both are the same. The following values are
measured in minutes.
Big Bank (three lines): 4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0 - ANSWER
mean= sum of all values/total number value
sum: 79.2
number of values: 11
mean: 7.2
median: 6th
7.2
equal
After recording the pizza delivery times for two different pizza shops, you conclude
that one pizza shop has a mean delivery time of
44
minutes with a standard deviation of
