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Median Calculation

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Median Calculation


1. **State the problem:** Find the median of the data set: $-28, -28, -23, -12, -2, 8, -16, 14, 6, -3, -16, -24$. 2. **Recall the definition of median:** The median is the middle value of a data set when the numbers are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers. 3. **Arrange the data in ascending order:** $$-28, -28, -24, -23, -16, -16, -12, -3, -2, 6, 8, 14$$ 4. **Count the number of data points:** There are 12 numbers, which is an even number. 5. **Find the two middle positions:** For 12 numbers, the middle positions are the 6th and 7th numbers. 6. **Identify the 6th and 7th numbers:** The 6th number is $-16$ and the 7th number is $-12$. 7. **Calculate the median:** $$\text{Median} = \frac{-16 + (-12)}{2} = \frac{-28}{2} = -14$$ **Final answer:** The median of the data set is $-14$.