Question 1

Shown below are the boxplot,the histogram and summary statistics for the weekly salaries (in dollars)of 24 randomly selected employees of a company:  $$\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 24 & 978.8 & 705 & 765.7 & 310 & 3700 & 510 & 1225
\end{array}$$ Write a few sentences describing the distribution.
A)The distribution is unimodal and skewed to the right.As shown in the boxplot,there are two outliers,weekly salaries of $2500 and about $3700.The median was 978.8,while the mean was 705,above the median score.The middle 50% of the weekly salaries were between $510 and $1225 for an IQR of $715.
B)The distribution is bimodal and skewed to the right.As shown in the boxplot,there are two outliers,weekly salaries of $2500 and about $3700.The median was 705,while the mean was 978.8,above the median score.The middle 50% of the weekly salaries were between $705 and $1225 for an IQR of $520.
C)The distribution is unimodal and skewed to the left.As shown in the boxplot,there are two outliers,weekly salaries of $2500 and about $3700.The median was 705,while the mean was 978.8,above the median score.The middle 50% of the weekly salaries were between $705 and $1225 for an IQR of $520.
D)The distribution is unimodal and skewed to the right.As shown in the boxplot,there are two outliers,weekly salaries of $2500 and about $3700.The median was 705,while the mean was 978.8,above the median score.The middle 50% of the weekly salaries were between $510 and $1225 for an IQR of $715.
E)The distribution is unimodal and skewed to the left.As shown in the boxplot,there are two outliers,weekly salaries of $2500 and about $3700.The median was 705,while the mean was 978.8,above the median score.The middle 50% of the weekly salaries were between $510 and $1225 for an IQR of $715.

Accepted Answer

The distribution is clearly unimodal and skewed to the right, as evidenced by the histogram and boxplot. The outliers are also present and notable in the plot. The summary statistics also support this, with a median of 705 and a mean of 978.8, indicating that the distribution is skewed to the right. The IQR of 715 also supports this interpretation. Therefore, Choice D is the best option.

Question 2

A medical study of the effects of on Drug X asked adult volunteers to take a heart-rate test one hour after taking Drug X.Some took a placebo (a pill containing no active ingredients),some were given a regular dose of Drug X,and others were given half a regular dose of Drug X.Here are the 5-number summaries for each group's scores on the test (# of beats that the heart rate increased when timed for 60 seconds): $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline & \mathrm { n } & \mathrm { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \
\hline \text { Placebo } & 13 & 0 & 1 & 2 & 3 & 5 \
\hline \text { Half Dose } & 13 & 1 & 2 & 3 & 5 & 8 \
\hline \text { Reg. Dose } & 13 & 1 & 2 & 3 & 7 & 9 \
\hline
\end{array}$$ a)Describe the W's for these data.
b)Name the variables and classify each as categorical or quantitative.
c)Write a few sentences comparing the results of the three groups (create parallel boxplots to help you,if necessary.)

Accepted Answer

The answer of A medical study of the effects of...

Question 3

Shown below are the boxplot,the histogram and summary statistics for the highest temperatures ever recorded (in °F)in 32 different states in the U.S.A..  $$\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 32 & 114.2 & 114.5 & 7.7 & 100 & 134 & 107.5 & 118
\end{array}$$ Write a few sentences describing the distribution.
A)The distribution is bimodal,symmetric with a mean of 114.2°F.There is a high outlier that should be investigated.The standard deviation is 7.7°F.The boxplot shows that half of the time,the highest temperatures were between about 107.5°F and 114°F.
B)The distribution is unimodal,symmetric enough with a mean of 114.2°F.There is a high outlier that should be investigated,but it does not influence the mean very much.The standard deviation is 7.7°F.The boxplot shows that half of the time,the highest temperatures were between about 107.5°F and 118°F.
C)The distribution is bimodal,essentially symmetric with a mean of 114.2°F.There is a high outlier that should be investigated,but it does not influence the mean very much.The standard deviation is 7.7°F.The boxplot shows that half of the time,the highest temperature were between about 107.5°F and 118°F.
D)The distribution is unimodal,essentially symmetric with a mean of 114.2°F.There is a high outlier that should be investigated,because it influences the mean.The standard deviation is 7.7°F.The boxplot shows that half of the time,the highest temperatures were between about 107.5°F and 114°F.
E)The distribution is unimodal,essentially symmetric with a mean of 114.2°F.There is a high outlier that should be investigated,but it does not influence the mean very much.The standard deviation is 7.7°F.The boxplot shows that half of the time,the highest temperatures were between about 107.5°F and 114°F.

Accepted Answer

The answer of Shown below are the boxplot,the histogram and...

Question 4

Here are summary statistics for the time,in minutes,it took for 20 people to complete an information survey at a walk-in medical clinic. $$\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 20 & 3.23 & 3.45 & 1.2 & 0.4 & 7.0 & 2.1 & 3.8
\end{array}$$ Write a few sentences about the amount of time these people took to complete the information survey.
A)The 20 times range in length between 0.4 and 7 minutes.The median time is 3.45 minutes,so half are longer and half are shorter.The middle 50% of these times range between 2.1 and 3.8 minutes.The distribution is skewed to the right,with at least the outlier 0.4 minutes.
B)The 20 times range in length between 0.4 and 7 minutes.The median time is 3.23 minutes,so half are longer and half are shorter.The middle 50% of these times range between 2.1 and 3.45 minutes.The distribution is skewed to the right,with at least the outlier 7 minutes.
C)The 20 times range in length between 0.4 and 7 minutes.The median time is 3.45 minutes,so half are longer and half are shorter.The middle 50% of these times range between 2.1 and 3.8 minutes.The distribution is skewed to the right,with no outliers.
D)The 20 times range in length between 0.4 and 7 minutes.The median time is 3.45 minutes,so half are longer and half are shorter.The middle 50% of these times range between 0.4 and 3.8 minutes.The distribution is skewed to the left,with at least the outlier 0.4 minutes.
E)The 20 times range in length between 0.4 and 7 minutes.The median time is 3.45 minutes,so half are longer and half are shorter.The middle 50% of these times range between 2.1 and 3.8 minutes.The distribution is skewed to the left,with at least the outlier 7 minutes.

Accepted Answer

The answer of Here are summary statistics for the time,in...

Question 5

Here are summary statistics for the time,in minutes,it took for 20 people to complete an information survey at a walk-in medical clinic. $$\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 20 & 3.23 & 3.45 & 1.2 & 0.4 & 7.0 & 2.1 & 3.8
\end{array}$$ Would you describe this distribution as symmetric or skewed?
A)Skewed to the left,because the mean is smaller than the median and the upper quartile is farther from the median than the lower quartile.
B)Skewed to the right,because the mean is smaller than the median and the lower quartile is farther from the median than the upper quartile.
C)Symmetric,because the mean and the median are close.
D)Skewed to the right,because the mean is larger than the median and the upper quartile is farther from the median than the lower quartile.
E)Skewed to the left,because the mean is smaller than the median and the lower quartile is farther from the median than the upper quartile.

Accepted Answer

The distribution is skewed to the left because the mean is smaller than the median and the lower quartile is farther from the median than the upper quartile.

Question 6

A class of sixth graders takes a diagnostic reading test,and the scores are reported by reading grade level.The 5-number summaries for the 20 boys and 21 girls are shown:
Boys: 4.7 5.9 6.4 7.6 7.8
Girls: 4.1 5.8 6.4 6.8 8.0
a)Which group had the highest score?
b)Which group had the greatest range?
c)Which group had the greatest interquartile range?
d)Which group's scores appear to be more skewed? Explain.
e)Which group generally did better on the test? Explain.
f)If the mean reading level for boys was 6.6 and for girls was 6.4,what is the overall mean for the class?

Accepted Answer

The answer of A class of sixth graders takes a...

Question 7

Shown below are the boxplot,the histogram and summary statistics for the weights (in pounds)of 30 newborn babies:  $$\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 30 & 6.9 & 7.0 & 0.8 & 5.5 & 8.7 & 6.4 & 7.7
\end{array}$$ Write a few sentences describing the distribution.
A)The distribution is unimodal and symmetric.There are no outliers.The mean newborn baby weight was $6.9 \mathrm { lb }$ with a standard deviation of 0.8 lb.
B)The distribution is unimodal and symmetric.There are no outliers.The mean newborn baby weight was $7 \mathrm { lb }$ with a standard deviation of 1.3 lb.
C)The distribution is unimodal and skewed to the right.There are no outliers.The mean newborn baby weight was $7 \mathrm { lb }$ with an IQR of 1.3 lb.
D)The distribution is bimodal and symmetric.There are no outliers.The mean newborn baby weight was $6.9 \mathrm { lb }$ with a standard deviation of 0.8 lb.
E)The distribution is unimodal and skewed to the left.There are no outliers.The mean newborn baby weight was $7 \mathrm { lb }$ with an IQR of 1.3 lb.

Accepted Answer

The boxplot shows a symmetric distribution with no outliers, and the histogram also suggests a unimodal distribution that is roughly symmetric. The summary statistics provide a mean and standard deviation, which are consistent with a roughly normal distribution.

Question 8

Here is the boxplot and an ogive of the distribution of students marks on their statistics test.  Write a few sentences describing this distribution.
A)The distribution of the marks is slightly skewed to the left.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 18 to 75,for an IQR of 57.55% of the students had a mark less than 50.
B)The distribution of the marks is slightly skewed to the left.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark less than 50.
C)The distribution of the marks is slightly skewed to the right.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark greater than 50.
D)The distribution of the marks is slightly skewed to the left.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark greater than 50.
E)The distribution of the marks is slightly skewed to the right.The median mark was about 55,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark less than 50.

Accepted Answer

The answer of Here is the boxplot and an ogive...

Quiz 3: Displaying and Summarizing Quantitative Data

Here is the boxplot and an ogive of the distribution of students marks on their statistics test. Write a few sentences describing this distribution.