Answer
Median = 17
Q1=8
Q3=25
IQR= 17
1.5*IQR= 25.5
Lower inner fence = -17.5
Upper inner fence=50.5
Smallest value within the two inner fences = 3
Largest value within the two inner fences =34
Work Step by Step
The ranked data in increasing order is as follows:
3,5,5,6,8,10,14,15,16,17,17,19,21,22,23,25,30,31,31,34
Median = (17+17)/2 = 17
Q1=8
Q3=25
IQR= Q3-Q1 = (25-8) = 17
To find the lower and upper inner fences,
1.5*IQR= (1.5*17) = 25.5
Lower inner fence = (Q1-25.5) = 8-25.5 = -17.5
Upper inner fence= (Q3+43.5) = 25+ 25.5 =50.5
Smallest value within the two inner fences = 3
Largest value within the two inner fences =34
According to to the box-and-whisker plot, about 50% of the data values fall within the box, about 25% fall on the left side of the box and about 25% fall on the right side of the box. Also, 50% of the values fall on the left side of the median and 50% lie on the right side of the median. The data of this example are skewed to the left because the upper 50% of the values are spread over a smaller range than the lower 50% of the values.
