To find the median of the given data set, we first need to arrange the numbers in ascending order:
The original data set is:
{10, 26, 14, 12.5, 13, 11, 12.5, 14.1, 11, 8, 14, 12.3, 11.4}
Arranging the data in ascending order:
{8, 10, 11, 11, 11.4, 12.3, 12.5, 12.5, 13, 14, 14.1, 14, 26}
Next, we count how many numbers are in the set. There are 13 numbers in total, which is odd.
To find the median in an odd data set, we locate the middle number. The middle number's position can be found using the formula:
\((n+1)/2\) where \(n\) is the number of data points.
So, \( (13 + 1) / 2 = 7 \).
The 7th number in the ordered list is:
{8, 10, 11, 11, 11.4, 12.3, 12.5, 12.5, 13, 14, 14.1, 14, 26}
Thus, the median hair length is 12.5 inches.