Question

Consider the following 8 numbers, where one labelled X is unknown.
17, 18, 24, X, 44, 48, 42, 4
Given that the range of the numbers is 51,
work out 2 values of X.

Answer 1

Answer:

$55,-3$

Step-by-step explanation:

$We\ are\ given\ that,\\There\ are\ eight\ numbers\ in\ the\ data :\\17,18,24,x,44,48,42,4\\Where\ the\ value\ of\ x\ is\ what\ we\ need\ to\ find.\\Range\ of\ the\ data=51\\Hence,\\We\ know\ that\ the\ range\ is\ the\ difference\\ between\ the\ highest\ observation\ and\ the\ lowest\ observation\ in\ the\ data.\\We\ may\ know\ see\ two\ cases\ of\ evaluating\ x\ when:\\1. x\ is\ the\ highest\ observation\ in\ the\ data\ or\ x>48.\\Highest\ observation\ =x\\Lowest\ observation=4\\Hence,$

$As\ range=51,\\x-4=51\\x=51+4\ [Adding\ 4\ on\ both\ the\ sides]\\x=55 \\2. x\ is\ the\ lowest\ observation\ or\ x<4.\\Hence,\\Highest\ observation=48\\Lowest\ observation=x\\Hence,\\As\ the\ range\ is\ 51,\\48-x=51\\-x=51-48 [Subtracting\ 48\ from\ both\ the\ sides]\\-x=3\\x=-3$