To determine the median temperature from the provided data, we need to follow a structured approach. Here's the step-by-step solution:
1. List all the temperatures given in the table:
[tex]\[
27.6, 27.8, 26.2, 26.8, 27.6, 26.6, 27.3, 27.1, 27.4, 27.3, 27.2, 27.7, 26.9
\][/tex]
2. Arrange the temperatures in ascending order:
[tex]\[
26.2, 26.6, 26.8, 26.9, 27.1, 27.2, 27.3, 27.3, 27.4, 27.6, 27.6, 27.7, 27.8
\][/tex]
3. Count the number of temperatures ([tex]\(n\)[/tex]):
[tex]\[
n = 13
\][/tex]
4. Calculate the median:
- Since [tex]\(n\)[/tex] is an odd number, the median is the middle element in the list.
- The middle element in a sorted list can be found using the formula:
[tex]\[
\text{Median} = \text{Value at position} \left(\frac{n + 1}{2}\right)
\][/tex]
- For [tex]\(n = 13\)[/tex]:
[tex]\[
\text{Median Position} = \left(\frac{13 + 1}{2}\right) = 7
\][/tex]
5. Find the value at the 7th position in the sorted list:
[tex]\[
26.2, 26.6, 26.8, 26.9, 27.1, 27.2, \underline{27.3}, 27.3, 27.4, 27.6, 27.6, 27.7, 27.8
\][/tex]
Therefore, the median temperature for the data shown in the table is [tex]\(27.3^{\circ} C\)[/tex].
