Answer: ![Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100](https://tex.z-dn.net/?f=Min%20%3A%20%24750%5C%20%2C%5C%20Q_1%3D%20%5C%24800%5C%20%2C%5C%20Median%20%3A%20%5C%24925%5C%20%2C%5C%20Q_3%3D%5C%241050%5C%20%2C%5C%20Max%3A%20%5C%241100)
Step-by-step explanation:
The five -number summary consists of five values :
Minimum value , First quartile
, Median , Third Quartile
, 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![=\dfrac{900+950}{2}=\$925](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B900%2B950%7D%7B2%7D%3D%5C%24925)
First quartile
= Median of lower half ($750,$800, $900)
= $800
, Third Quartile
= 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 :
![Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100](https://tex.z-dn.net/?f=Min%20%3A%20%24750%5C%20%2C%5C%20Q_1%3D%20%5C%24800%5C%20%2C%5C%20Median%20%3A%20%5C%24925%5C%20%2C%5C%20Q_3%3D%5C%241050%5C%20%2C%5C%20Max%3A%20%5C%241100)