To find the median of a list of temperatures (or any set of numbers), follow these steps:
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Organize the Data: Arrange the list of temperatures in ascending order from the smallest to the largest.
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Count the Numbers: Determine the total number of temperatures in the list.
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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: \[ \text{Median indices} = \frac{n}{2} - 1 \quad \text{and} \quad \frac{n}{2} \]
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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.
- Organize the Data: 68, 70, 72, 74, 75
- Count the Numbers: There are 5 temperatures (n=5).
- 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:
- Organize the Data: 68, 70, 72, 73, 74, 75
- Count the Numbers: There are 6 temperatures (n=6).
- 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.