Question

the median for the given set of six ordered data values is 28.5. 7 12 23 _ 41 50 what is the missing value? the missing value is (type an integer or a decimal.)

Explanation:

Step1: Recall median formula for even - numbered data

For a set of $n = 6$ (even - numbered) ordered data values $x_1,x_2,\cdots,x_6$, the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$. Here, $n = 6$, so the median is the average of the 3rd and 4th ordered values. Let the missing value be $x$. The 3rd value is 23 and the 4th value is $x$.

Step2: Set up the equation for the median

We know that $M = 28.5$ and $M=\frac{23 + x}{2}$. So, we set up the equation $\frac{23 + x}{2}=28.5$.

Step3: Solve the equation for $x$

Multiply both sides of the equation by 2: $23 + x=28.5\times2$.
$23 + x = 57$.
Subtract 23 from both sides: $x=57 - 23$.
$x = 34$.

Answer:

34