Given a data set has a Median of 10 and an Inner Quartile Range of 5, what is the range of values that Q3 could possibly be?
2 answers:
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Answer:
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Step-by-step explanation:
This exercise is an example of <em>linear system equations</em>. A <em>system of linear equations</em> is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.
The easy way to solve this problem is by using the<em> reduction method</em>.The <em>reduction method</em> consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.
Ordering the equations as a system equations.
Using the reduction method, let's substract the second equation with the first equation, in order to clear m.
600m + b = 11250
<u>-400m - b = -7650</u>
200m = 3600 --------> m = 3600/200 -----> m = 18
We can substitute the value of m in any of the two equations to obtain the unknow b.
Let's substitute the value of m in the second equation.
400(18) + b = 7650
7200 + b = 7650 -----> b = 7650 - 7200 -------> b = 450
We can check this values in both equations.
600m + b = 11250 -----> 600(18) + 450 = 11250
400m + b = 7650 -----> 400(18) + 450 = 7650
Satisfying the result of both equations.