Quantitative Reasoning Exams (Latest 2024/ 2025
Updates STUDY BUNDLE PACKAGE WITH SOLUTIONS)
Questions and Verified Answers| 100% Correct| Grade
A
If X is correlated with Y, what must be true about X and Y? Explain your reasoning. -
ANSWERIncreasing 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.
- - ANSWEREvidence 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 the second-hand smoke is a cause of
the birth defects.
Suppose you are given the mean and just one data value from a distribution. What
can you calculate? - ANSWERThe 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? - ANSWERThe heights of all elementary-school children, since it has
the largest range.
Describe how the range of a distribution is defined and calculated. - ANSWERThe
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? - ANSWERThe 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. - ANSWERThe
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. - ANSWERThe 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. - ANSWERThe 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 - ANSWERmean=
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
4
minutes. The other shop has a mean delivery time of
41
minutes with a standard deviation of
22
minutes. Interpret these figures. If you liked the pizzas from both shops equally well,
which one would you order from? Why? - ANSWER- The means are nearly equal, but
the variation is significantly greater for the second shop than for the first.
- Choose the first shop. The delivery time is more reliable because it has a lower
standard deviation.
Two airlines have data on the arrival times of their flights. An arrival time of +6
minutes means the flight arrived
6 minutes early. An arrival time of −3 minutes means the flight arrived
3 minutes late. Skyview Airlines has a mean arrival time of 1.5 minutes with a
standard deviation of 10.7 minutes. SkyHigh Airlines has a mean arrival time of −4
minutes with a standard deviation of 5 minutes. Explain the meaning of these figures
and why they would affect your choice of airline. - ANSWERIf you want to avoid long
delays,
SkyHigh Airlines might be the better choice.
SkyHigh Airlines on average runs slightly behind schedule, but it tends to have
smaller delays. While
Updates STUDY BUNDLE PACKAGE WITH SOLUTIONS)
Questions and Verified Answers| 100% Correct| Grade
A
If X is correlated with Y, what must be true about X and Y? Explain your reasoning. -
ANSWERIncreasing 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.
- - ANSWEREvidence 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 the second-hand smoke is a cause of
the birth defects.
Suppose you are given the mean and just one data value from a distribution. What
can you calculate? - ANSWERThe 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? - ANSWERThe heights of all elementary-school children, since it has
the largest range.
Describe how the range of a distribution is defined and calculated. - ANSWERThe
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? - ANSWERThe 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. - ANSWERThe
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. - ANSWERThe 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. - ANSWERThe 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 - ANSWERmean=
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
4
minutes. The other shop has a mean delivery time of
41
minutes with a standard deviation of
22
minutes. Interpret these figures. If you liked the pizzas from both shops equally well,
which one would you order from? Why? - ANSWER- The means are nearly equal, but
the variation is significantly greater for the second shop than for the first.
- Choose the first shop. The delivery time is more reliable because it has a lower
standard deviation.
Two airlines have data on the arrival times of their flights. An arrival time of +6
minutes means the flight arrived
6 minutes early. An arrival time of −3 minutes means the flight arrived
3 minutes late. Skyview Airlines has a mean arrival time of 1.5 minutes with a
standard deviation of 10.7 minutes. SkyHigh Airlines has a mean arrival time of −4
minutes with a standard deviation of 5 minutes. Explain the meaning of these figures
and why they would affect your choice of airline. - ANSWERIf you want to avoid long
delays,
SkyHigh Airlines might be the better choice.
SkyHigh Airlines on average runs slightly behind schedule, but it tends to have
smaller delays. While
