Question 1

Provide an appropriate response.
-Given the following five-number summary, find the IQR. $\begin{array} { l l l l l } 2.9 , & 5.7 , & 10.0 , & 13.2 , & 21.1 \text {. } \end{array}$
A) $7.5$
B) $7.1$
C) $11.1$
D) $18.2$

Accepted Answer

The Interquartile Range (IQR) is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). From the given five-number summary, Q3 = 13.2 and Q1 = 5.7. Therefore, IQR = 13.2 - 5.7 = 7.5.

Question 2

Draw and Interpret Boxplots
-The boxplot shown below was constructed in Excel for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local bottling company.  Based on the information given in the boxplot below, what shape do you believe the data to have
A) skewed to the left
B) approximately symmetric
C) skewed to the right
D) cannot be determined

Accepted Answer

The answer of Draw and Interpret Boxplots
-The boxplot shown below...

Question 3

Provide an appropriate response.
-The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find any outliers and provide an explanation for them. $$\begin{array} { l l l l l } 
0.4 & 1.0 & 1.5 & 1.6 & 2.0 \
2.2 & 2.4 & 2.7 & 3.4 & 3.4 \
3.5 & 3.6 & 3.6 & 3.7 & 3.7 \
3.9 & 4.1 & 4.2 & 4.2 & 7.0
\end{array}$$

Accepted Answer

The answer of Provide an appropriate response.
-The normal monthly precipitation...

Question 4

Provide an appropriate response.
-The following is a sample of 19 November utility bills (in dollars) from a neighborhood: $52,62,66,68,72,74,74,76,76,76,78,78,82,84,84,86,88,92,96$. Find the five -number summary.

Accepted Answer

The answer of Provide an appropriate response.
-The following is a...

Question 5

Provide an appropriate response.
-Eleven high school teachers were asked to give the number of students in their classes. The sample data follows. Would any of the class sizes be considered an outlier? Answer Yes or No.
36, 31, 30, 31, 20, 19, 24, 34, 21, 28, 24
A) No
B) Yes

Accepted Answer

The data set does not have any extreme values that are significantly different from the rest, so there are no outliers.

Question 6

Provide an appropriate response.
-An Excel printout of some descriptive statistics for a set of data is shown below. What is the IQR 
A) $15.5$
B) 15
C) 38
D) $5.5$

Accepted Answer

The answer of Provide an appropriate response.
-An Excel printout of...

Question 7

Draw and Interpret Boxplots
-A survey of 200 public universities indicated that the 25th percentile of the yearly tuition cost of the universities was $4500 and the 75th percentile was $7800. The minimum value was $2000, the median was $6000, and the maximum was $10,000. Use this information to construct a boxplot for the yearly tuition costs.

Accepted Answer

The answer of Draw and Interpret Boxplots
-A survey of 200...

Question 8

Draw and Interpret Boxplots
-The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Draw a boxplot that represents the data. $$\begin{array} { l l l l l l l l l l } 
154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \
189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \
205 & 205 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 275
\end{array}$$

Accepted Answer

The answer of Draw and Interpret Boxplots
-The cholesterol levels (in...

Question 9

Provide an appropriate response.
-Given the following five-number summary, find Q3. 2.9, $\quad 5.7 , \quad 10.0 , \quad 13.2 , \quad 21.1$.
A) $13.2$
B) $5.7$
C) $10.0$
D) $21.1$

Accepted Answer

Q3, or the third quartile, is the value that separates the highest 25% of the data from the rest. In a five-number summary, Q3 is explicitly given as the fourth number, which is 13.2 in this case.

Question 10

Draw and Interpret Boxplots
-The test scores of 30 students are listed below. Draw a boxplot that represents the data. $$\begin{array} { l l l l l l l l l l } 
31 & 41 & 45 & 48 & 52 & 55 & 56 & 56 & 63 & 65 \
67 & 67 & 69 & 70 & 70 & 74 & 75 & 78 & 79 & 79 \
80 & 81 & 83 & 85 & 85 & 87 & 90 & 92 & 95 & 99
\end{array}$$

Accepted Answer

The answer of Draw and Interpret Boxplots
-The test scores of...

Question 11

Provide an appropriate response.
-A group of 79 students were asked how far they commute to work from home each time they go to work from home. The results are given below. Would a drive of 15 miles be considered an outlier Answer Yes or No. $\begin{array}{|c|c|}
\hline \begin{array}{c}
\text { Miles } \
\text { traveled }
\end{array} & \text { Frequency } \
\hline 1 & 1 \
\hline 2 & 2 \
\hline 3 & 12 \
\hline 4 & 18 \
\hline 5 & 7 \
\hline 6 & 10 \
\hline 7 & 10 \
\hline 8 & 11 \
\hline 9 & 5 \
\hline 10 & 3 \
\hline
\end{array}$

A) Yes
B) $\mathrm { No }$

Accepted Answer

A drive of 15 miles is significantly higher than the maximum distance recorded in the data (10 miles), making it an outlier.

Question 12

Draw and Interpret Boxplots
-SAS was used to compare the high school dropout rates for the 50 states in 1982 and 1984. The box plots generated for these dropout rates are shown below. Compare the center of the distributions and the variation of the distributions for the two years. 
A) Dropout rates had a higher average with less variability in 1982 than in 1984.
B) Dropout rates had a higher average with more variability in 1982 than in 1984.
C) Dropout rates had a lower average with more variability in 1982 than in 1984.
D) Dropout rates had a lower average with less variability in 1982 than in 1984.

Accepted Answer

The answer of Draw and Interpret Boxplots
-SAS was used to...

Question 13

Provide an appropriate response.
-Eleven high school teachers were asked to give the numbers of students in their classes. The sample data follows: $36,31,30,31,20,19,24,34,21,28$, 24. Find the five-number summary.

Accepted Answer

The answer of Provide an appropriate response.
-Eleven high school teachers...

Question 14

Provide an appropriate response.
-Given the following five-number summary, find the interquartile range. 
A) 29
B) 50 
C) 65
D) $32.5$

Accepted Answer

The answer of Provide an appropriate response.
-Given the following five-number...

Question 15

Provide an appropriate response.
-The selling prices of mutual funds change daily. In order to study these changes, a sample of mutual funds was examined and the daily changes in price are listed below.
$$0.05,0.00 , - 0.03 , - 0.01,0.18,0.00,0.02,0.29,0.00 , - 0.07,0.10,0.07,0.03$$
Determine the lower and upper fences. Are there any outliers according this criterion?

Accepted Answer

The answer of Provide an appropriate response.
-The selling prices of...

Question 16

Provide an appropriate response.
-A random sample of sale prices of homes yielded the following summary information: $$\begin{array} { l l l } 
\text { MIN } \$ 42,000 & 25 \% : \$ 81,000 & \text { Median: } \$ 138,000 \
\text { MAX } \$ 271,000 & 75 \% : \$ 169,000 &
\end{array}$$ Comment on a home that had a sale price of $415,000.
A) This value falls outside the upper fence and is considered an outlier.
B) This sale price would be expected since it falls inside the lower and upper fences.
C) This sale price falls between the lower and upper fences. It can be considered a potential outlier.
D) This value falls outside of the third quartile, but cannot be considered an outlier.

Accepted Answer

To determine if a value is an outlier, we calculate the interquartile range (IQR) and then the upper fence. IQR = Q3 - Q1 = $169,000 - $81,000 = $88,000. The upper fence is Q3 + 1.5*IQR = $169,000 + 1.5*$88,000 = $301,000. Since $415,000 is greater than the upper fence, it is considered an outlier.

Question 17

Provide an appropriate response.
-The following is a sample of 19 November utility bills (in dollars) from a neighborhood. What is the largest bill in the sample that would not be considered an outlier?
$52,62,66,68,72,74,76,76,76,78,78,82,84,84,86,88,92,96,110$
A) $\$ 96$
B) $\$ 95$
C) $\$ 88$
D) $\$ 86$

Accepted Answer

To determine the largest bill that would not be considered an outlier, we first calculate the interquartile range (IQR). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). For this data set:- Q1 (25th percentile) is between 72 and 74, so Q1 = 73.- Q3 (75th percentile) is between 84 and 86, so Q3 = 85.- IQR = Q3 - Q1 = 85 - 73 = 12.An outlier is defined as a value that is more than 1.5 times the IQR above the third quartile or below the first quartile. The upper bound for non-outliers is Q3 + 1.5*IQR = 85 + 1.5*12 = 85 + 18 = 103.Therefore, the largest bill that would not be considered an outlier is $96, as it is less than the upper bound of 103.

Question 18

Draw and Interpret Boxplots
-In interpreting a boxplot of a data set we note that the median is to the left of the center of the box and the right line is longer than the left line. We can conclude that
A) The data is skewed right.
B) The data is skewed left.
C) The data is symmetric.
D) Skewness or symmetry cannot be determined by a box plot.

Accepted Answer

When the median is closer to the left side of the box and the right whisker (line) is longer than the left whisker, it indicates that the data distribution has a longer tail on the right side, suggesting a right-skewed (or positively skewed) distribution.

Quiz 3: Numerically Summarizing Data

Provide an appropriate response. -Given the following five-number summary, find the IQR. $\begin{array} { l l l l l } 2.9 , & 5.7 , & 10.0 , & 13.2 , & 21.1 \text {. } \end{array}$

Draw and Interpret Boxplots -The boxplot shown below was constructed in Excel for the amount of soda that was poured by a filling machine into 12-ounce soda cans at a local bottling company. Based on the information given in the boxplot below, what shape do you believe the data to have

Provide an appropriate response. -The following is a sample of 19 November utility bills (in dollars) from a neighborhood: $52,62,66,68,72,74,74,76,76,76,78,78,82,84,84,86,88,92,96$ . Find the five -number summary.

Provide an appropriate response. -Eleven high school teachers were asked to give the number of students in their classes. The sample data follows. Would any of the class sizes be considered an outlier? Answer Yes or No. 36, 31, 30, 31, 20, 19, 24, 34, 21, 28, 24

Provide an appropriate response. -An Excel printout of some descriptive statistics for a set of data is shown below. What is the IQR

Provide an appropriate response. -Given the following five-number summary, find Q3. 2.9, $\quad 5.7 , \quad 10.0 , \quad 13.2 , \quad 21.1$ .

Draw and Interpret Boxplots -SAS was used to compare the high school dropout rates for the 50 states in 1982 and 1984. The box plots generated for these dropout rates are shown below. Compare the center of the distributions and the variation of the distributions for the two years.

Provide an appropriate response. -Eleven high school teachers were asked to give the numbers of students in their classes. The sample data follows: $36,31,30,31,20,19,24,34,21,28$ , 24. Find the five-number summary.

Provide an appropriate response. -Given the following five-number summary, find the interquartile range.

Provide an appropriate response. -The following is a sample of 19 November utility bills (in dollars) from a neighborhood. What is the largest bill in the sample that would not be considered an outlier? $52,62,66,68,72,74,76,76,76,78,78,82,84,84,86,88,92,96,110$

Draw and Interpret Boxplots -In interpreting a boxplot of a data set we note that the median is to the left of the center of the box and the right line is longer than the left line. We can conclude that