Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
-The weights (in ounces) of 27 tomatoes are listed below. $\begin{array} { l l l l l l l l l } 1.7 & 2.0 & 2.2 & 2.2 & 2.4 & 2.5 & 2.5 & 2.5 & 2.6 \ 2.6 & 2.6 & 2.7 & 2.7 & 2.7 & 2.8 & 2.8 & 2.8 & 2.9 \ 2.9 & 2.9 & 3.0 & 3.0 & 3.1 & 3.1 & 3.3 & 3.6 & 4.2 \end{array}$
A) Outliers: $1.7 \mathrm { oz } , 3.6 \mathrm { oz } , 4.2 \mathrm { oz }$
B) Outliers: $1.7 \mathrm { oz } , 4.2 \mathrm { oz }$
C) Outlier: $4.2 \mathrm { oz }$
D) No outliers

Question

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
-The weights (in ounces) of 27 tomatoes are listed below. $\begin{array} { l l l l l l l l l } 1.7 & 2.0 & 2.2 & 2.2 & 2.4 & 2.5 & 2.5 & 2.5 & 2.6 \ 2.6 & 2.6 & 2.7 & 2.7 & 2.7 & 2.8 & 2.8 & 2.8 & 2.9 \ 2.9 & 2.9 & 3.0 & 3.0 & 3.1 & 3.1 & 3.3 & 3.6 & 4.2 \end{array}$
A) Outliers: $1.7 \mathrm { oz } , 3.6 \mathrm { oz } , 4.2 \mathrm { oz }$ 
B) Outliers: $1.7 \mathrm { oz } , 4.2 \mathrm { oz }$ 
C) Outlier: $4.2 \mathrm { oz }$ 
D) No outliers

Quizplus · Accepted Answer

To construct a boxplot, we need to find the minimum value, maximum value, median, and quartiles of the data. The five-number summary of the given data is:
Minimum: 1.7 oz
First Quartile (Q1): 2.5 oz
Median (Q2): 2.8 oz
Third Quartile (Q3): 3.1 oz
Maximum: 4.2 oz

The interquartile range (IQR) is the difference between the third and first quartiles: IQR = Q3 - Q1 = 3.1 - 2.5 = 0.6

To identify outliers, we need to find values that are less than Q1 - 1.5 IQR or greater than Q3 + 1.5 IQR. 
Q1 - 1.5 IQR = 2.5 - 1.5(0.6) = 1.6
Q3 + 1.5 IQR = 3.1 + 1.5(0.6) = 4.1

The data values 1.7 oz and 4.2 oz are less than 1.6 and greater than 4.1, respectively. These are the outliers.

Among the answer choices, only option B correctly identifies the outliers as 1.7 oz and 4.2 oz. Option A includes an extra outlier of 3.6 oz, which is not valid. Option C identifies only one outlier, while there are two outliers in the data. Option D is not a correct choice because there are outliers in the data.

Construct a Boxplot for the Given Data A) Outliers 1.7oz,3.6oz,4.2oz1.7 \mathrm { oz } , 3.6 \mathrm { oz } , 4.2 \mathrm { oz }1.7oz,3.6oz,4.2oz

Construct a Boxplot for the Given Data A) Outliers $1.7 \mathrm { oz } , 3.6 \mathrm { oz } , 4.2 \mathrm { oz }$