To find the median length, follow these steps:
1. List the lengths in ascending order: Start by arranging the given lengths in increasing order:
[tex]\[
7.3, 10.4, 11.8, 12.3, 14.7
\][/tex]
2. Find the position of the median: The median is the middle value in a list of numbers arranged in order. Since there are five numbers (an odd number), the median is the one in the middle position. The middle position can be found by calculating:
[tex]\[
\text{Middle Position} = \left(\frac{n + 1}{2}\right)^{th} \text{term}
\][/tex]
where [tex]\( n \)[/tex] is the number of terms. For our list of five numbers:
[tex]\[
\text{Middle Position} = \left(\frac{5 + 1}{2}\right) = \frac{6}{2} = 3^{rd} \text{term}
\][/tex]
3. Identify the third term: Now, look at the sorted list and identify the third term.
[tex]\[
7.3, 10.4, \boxed{11.8}, 12.3, 14.7
\][/tex]
So, the median length of the pencils is [tex]\( 11.8 \)[/tex] cm.
