Question

what is the median of the following set of numbers?
\\(\frac{1}{12}\\), \\(\frac{5}{12}\\), \\(\frac{1}{2}\\), \\(\frac{1}{6}\\), \\(\frac{1}{2}\\), \\(\frac{3}{4}\\), \\(\frac{2}{3}\\)
a. \\(\frac{2}{3}\\)
b. \\(\frac{11}{24}\\)
c. \\(\frac{1}{2}\\)
d. \\(\frac{5}{12}\\)

Explanation:

Step1: Convert to common denominator

Rewrite all fractions with denominator 12:
$\frac{1}{12}$, $\frac{5}{12}$, $\frac{6}{12}$, $\frac{2}{12}$, $\frac{6}{12}$, $\frac{9}{12}$, $\frac{8}{12}$

Step2: Sort the values

Arrange from smallest to largest:
$\frac{1}{12}$, $\frac{2}{12}$, $\frac{5}{12}$, $\frac{6}{12}$, $\frac{6}{12}$, $\frac{8}{12}$, $\frac{9}{12}$

Step3: Find the middle value

For 7 terms, the 4th term is the median:
$\frac{6}{12} = \frac{1}{2}$

Answer:

C. $\frac{1}{2}$