Answer: [tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]
Step-by-step explanation:
The five -number summary consists of five values :
Minimum value , First quartile [tex](Q_1)[/tex] , Median , Third Quartile [tex](Q_3)[/tex] , Maximum value.
Given : The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions.
The following costs are for a sample of six cars:
$800, $750, $900, $950, $1100, $1050.
Arrange data in increasing order :
$750,$800, $900, $950, $1050, $1100
Minimum value = $750
Maximum value = $1100
Median = middle most term
Since , total observation is 6 (even) , so Median = Mean of two middle most values ($900 and $950).
i.e. Median[tex]=\dfrac{900+950}{2}=\$925[/tex]
First quartile [tex](Q_1)[/tex] = Median of lower half ($750,$800, $900)
= $800
, Third Quartile [tex](Q_3)[/tex] = Median of upper half ($950, $1050, $1100)
= $1050
Hence, the five-number summary of the total damage suffered for this sample of cars will be :
[tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]
