Question

some of the students at syracuse junior high school work as volunteers at a homeless shelter. the table shows the number of hours the students volunteered during may.
hours worked 10 9 11 8 13 11 17 10 14 10 11
volunteer sam alicia pat cam erin mike jewel andrew pete zach tom
(a) find the five - number summary and iqr of the data.
min q1 med q3 max iqr
(b) use the five - number summary to test for outliers.
give the lower fence and upper fence.
list the name(s) of any student who is an outlier. if there are no outliers, type dne (for does not exist.)
lower fence upper fence outlier(s)

Explanation:

Step1: Arrange data in ascending order

8, 9, 10, 10, 10, 10, 11, 11, 11, 13, 14, 17

Step2: Find the minimum

The minimum value (Min) is 8.

Step3: Find the first - quartile (Q1)

There are 12 data points. The position of Q1 is $\frac{12 + 1}{4}=3.25$. So, Q1 is the value between the 3rd and 4th ordered data points. $Q1=\frac{10 + 10}{2}=10$.

Step4: Find the median (Med)

The position of the median for 12 data points is $\frac{12}{2}=6$ and $\frac{12}{2}+1 = 7$. So, $Med=\frac{10+11}{2}=10.5$.

Step5: Find the third - quartile (Q3)

The position of Q3 is $3\times\frac{12 + 1}{4}=9.75$. So, Q3 is the value between the 9th and 10th ordered data points. $Q3=\frac{11+13}{2}=12$.

Step6: Find the maximum

The maximum value (Max) is 17.

Step7: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1=12 - 10 = 2$.

Step8: Calculate the lower and upper fences

Lower fence: $Q1-1.5\times IQR=10-1.5\times2 = 7$.
Upper fence: $Q3 + 1.5\times IQR=12+1.5\times2=15$.

Step9: Identify outliers

Any value less than the lower fence or greater than the upper fence is an outlier. The value 17 is greater than 15, so Jewel is the outlier.

Answer:

Min: 8
Q1: 10
Med: 10.5
Q3: 12
Max: 17
IQR: 2
Lower fence: 7
Upper fence: 15
Outlier(s): Jewel