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# Quiz_2H_Boxplot

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```									           Biom 109                               Quiz 2H               Name_______________

Given a sorted data set reporting on the average weekly hours     8      35    58     70    72
75      82    88     89    89
that 28 students spend in front of a computer, summarize the     95      96   100    100   104
data set with a 7 number summary using correct notation and     106     106   108    108   112
complete sketch of a box plot on the number line provided       113     114   114    115   115
117     118   119
below. N = 28

This Data set is Circle one: 1.) Skewed left          2.) Symmetrical            3.) Skewed right
Biom 109                                     Quiz 2H                                  Key

Solution:

n  1 28  1                              ~  n  1  28  1  14.5th value
Q1                     7.25th value               x
4     4                                       2       2
th
14 value = 100, 15th value = 104,
7th value = 82, 8th value = 88, then:
th            th              th   th
Q2 = 14th val. + 0.5(15th – 14th)
7.25 value = 7 val. + 0.25(8 – 7 )                   ~
x 100 + 0.5(104 – 100)
7.25th value = 82 + 0.25(88 – 82)
7.25th value = 82 + 0.25(6)
~  102
x
7.25th value = 82 + 1.5
7.25th value = 83.5
IQR = Q3  Q1 = 113.75 – 83.5 = 30.25

then Q1  83 .5                                      Step = 1.5x IQR = 1.5x 30.25 = 43.375
3n  1 328  1                        Upper outlier threshold = Q3 + step
Q3                           21.75th value                                = 113.75 + 43.375
4        4
UOT = 159.125
21st value = 113, 22nd value = 114, then:
Lower outlier threshold = Q1 – step
21.75th value = 21st val. + 0.75(22nd – 21st )                               = 83.5 – 43.375
21.75th value = 113 + 0.75(27 – 26)                                          = 40.125
Min = 8
21.75th value = 113 + 0.75(1)                        Max = 119
21.75th value = 113 + 0.75
21.75th value = 113.75
Q3  113 .75

*                             *

Skewed Left

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