# Box and whisker plot

Construct a box and whisker plot for the given data.
56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43

Result

min =  12
Q1 =  23.5
Q2 =  33
Q3 =  46
max =  67

#### Solution:

$\{12, 19, 23, 23, 24, 32, 32, 32, 34, 36, 43, 45, 47, 54, 56, 67\} \ \\ min = 12$
$n = 16 \ \\ i_{ 1 } = n/4 = 16/4 = 4 \ \\ Q_{ 1 } = (23+24)/2 = \dfrac{ 47 }{ 2 } = 23.5$
$i_{ 2 } = n/2 = 16/2 = 8 \ \\ Q_{ 2 } = (32+34)/2 = 33$
$i_{ 3 } = 0.75 \cdot \ n = 0.75 \cdot \ 16 = 12 \ \\ Q_{ 3 } = (45+47)/2 = 46$
$max = 67$

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