Question

the median for the given set of six ordered data values is 31.5.
7 12 27 _ 41 51
what is the missing value?
the missing value is \boxed{}.

Explanation:

Step1: Recall median formula for even data

For \( n = 6 \) (even) data points, median is average of \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th values. So, median \( = \frac{\text{3rd value}+\text{4th value}}{2} \).

Step2: Identify known values

3rd value is \( 27 \), 4th is missing (\( x \)), median is \( 31.5 \). Substitute into formula: \( 31.5=\frac{27 + x}{2} \).

Step3: Solve for \( x \)

Multiply both sides by 2: \( 31.5\times2=27 + x \) → \( 63 = 27 + x \). Subtract 27: \( x = 63 - 27 = 36 \).

Answer:

36