Five number summary and IQR of both the data sets are different.
For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5
For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5
No, the box plots are not symmetric.
Part A:
The given data sets are
School A : 9,14,15,17,17,7,15,6,6
School B : 12,8,13,11,19,15,16,5,8
Arrange the data in ascending order.
School A : 6,6,7,9,14,15,15,17,17
School B : 5,8,8,11,12,13,15,16,19
Divide each data set into four equal parts.
School A : (6,6),(7,9),14,(15,15),(17,17)
School B : (5,8),(8,11),12,(13,15),(16,19)
For school A:
Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17
The interquartile range of the data is
For school B:
Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19
[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =16-6.2\\ =9.5[/tex]
The interquartile range of the data is
[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =15.5-8\\ =7.5[/tex]
Part B:
The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data sets are different.
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