Question

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.
1. What is the five-number summary of the total damage suffered for this sample of cars?

Answer 1

Answer: $Min : 750\ ,\ Q_1= \ 800\ ,\ Median : \ 925\ ,\ Q_3=\ 1050\ ,\ Max: \ 1100$

Step-by-step explanation:

The five -number summary consists of five values :

Minimum value , First quartile $(Q_1)$ , Median , Third Quartile $(Q_3)$  , 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$=\dfrac{900+950}{2}=\ 925$

First quartile $(Q_1)$ = Median of lower half ($750,$800, $900)

= $800

, Third Quartile $(Q_3)$  = 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 :

$Min : 750\ ,\ Q_1= \ 800\ ,\ Median : \ 925\ ,\ Q_3=\ 1050\ ,\ Max: \ 1100$