intro to stats 1.10 independent practice boxplots & outliers\n1. what are the five values in the five…

intro to stats 1.10 independent practice boxplots & outliers\n1. what are the five values in the five - number summary?\n2. in a boxplot, the width of the box is the inter quartile range\n3. here are the travel times in minutes for 15 workers in north carolina, chosen at random by the census bureau.\n30 20 10 40 25 20 10 60 15 40 5 30 12 10 10\na. identify any outliers.\n5,10,10,10,10,12,15,20,20,25,30,30,40,40,60\n↑\nq1 = 10\n20\n40\nb. give the five - number summary.\n|minimum|q1|median|q3|maximum|\n|----|----|----|----|----|\nc. make a boxplot.

intro to stats 1.10 independent practice boxplots & outliers\n1. what are the five values in the five - number summary?\n2. in a boxplot, the width of the box is the inter quartile range\n3. here are the travel times in minutes for 15 workers in north carolina, chosen at random by the census bureau.\n30 20 10 40 25 20 10 60 15 40 5 30 12 10 10\na. identify any outliers.\n5,10,10,10,10,12,15,20,20,25,30,30,40,40,60\n↑\nq1 = 10\n20\n40\nb. give the five - number summary.\n|minimum|q1|median|q3|maximum|\n|----|----|----|----|----|\nc. make a boxplot.

Answer

Explanation:

Step1: Arrange data in ascending order

$5, 10, 10, 10, 10, 12, 15, 20, 20, 25, 30, 30, 40, 40, 60$

Step2: Find the minimum value

The minimum value is $5$.

Step3: Calculate $Q1$

There are $n = 15$ data - points. The position of $Q1$ is $\frac{n + 1}{4}=\frac{15+1}{4}=4$. So, $Q1 = 10$.

Step4: Find the median

The position of the median is $\frac{n + 1}{2}=\frac{15 + 1}{2}=8$. So, the median is $20$.

Step5: Calculate $Q3$

The position of $Q3$ is $\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So, $Q3 = 30$.

Step6: Find the maximum value

The maximum value is $60$.

Step7: Identify outliers

The inter - quartile range $IQR=Q3 - Q1=30 - 10 = 20$. Lower fence $=Q1-1.5\times IQR=10-1.5\times20=10 - 30=-20$. Upper fence $=Q3 + 1.5\times IQR=30+1.5\times20=30 + 30 = 60$. Since all data - points are within the fences, there are no outliers.

Step8: Make a boxplot

On a number line, mark the minimum value ($5$), $Q1$ ($10$), the median ($20$), $Q3$ ($30$), and the maximum value ($60$). Draw a box from $Q1$ to $Q3$ with a line inside the box at the median. Draw whiskers from the box to the minimum and maximum values.

Answer:

a. There are no outliers. b.

Minimum $Q_1$ Median $Q_3$ Maximum
$5$ $10$ $20$ $30$ $60$
c. A boxplot with a box from $10$ to $30$, a line at $20$ inside the box, and whiskers extending to $5$ and $60$.