Question

How do you find the median of a list of temperatures?

Answer 1

To find the median of a list of temperatures (or any set of numbers), follow these steps:

1. **Organize the Data**: Arrange the list of temperatures in ascending order from the smallest to the largest.

2. **Count the Numbers**: Determine the total number of temperatures in the list.

3. **Find the Median**:
- If the total number of temperatures (n) is odd, the median is the middle number. You can find the index of the median using the formula:
\[
\text{Median index} = \frac{n}{2}
\]
(using zero-based indexing).
- If n is even, the median is the average of the two middle numbers. You find the indices as follows:
\[
\text{Median indices} = \frac{n}{2} - 1 \quad \text{and} \quad \frac{n}{2}
\]

4. **Calculate the Median**:
- For an odd n, the temperature at the median index is the median.
- For an even n, the median is the average of the temperatures at the two middle indices.

### Example

Consider the following list of temperatures: 72, 75, 68, 70, 74.

1. **Organize the Data**: 68, 70, 72, 74, 75
2. **Count the Numbers**: There are 5 temperatures (n=5).
3. **Find the Median**: Since 5 is odd, the median is the middle value, which is at index 2:
- Median = 72 (the third number in the ordered list).

If the list were: 72, 75, 68, 70, 74, 73:
1. **Organize the Data**: 68, 70, 72, 73, 74, 75
2. **Count the Numbers**: There are 6 temperatures (n=6).
3. **Find the Median**: Since 6 is even, find the average of the two middle values (at indices 2 and 3):
- Median = (72 + 73) / 2 = 72.5.

This is how you calculate the median temperature from a list.