The median of the following data is : 25, 15, 23, 25, 17, 27, 20, 18, 24, 30, 19, 28, 35, 10, 31, 40
24.5
To find the median of a given data set, we follow these steps:
- First, arrange the data in ascending order: \(10, 15, 17, 18, 19, 20, 23, 24, 25, 25, 27, 28, 30, 31, 35, 40\).
- Since the number of data points (\(n\)) is \(16\) (which is even), the median is the average of the \((n/2)\)th and \((n/2 + 1)\)th observations.
- Now, calculate \(n/2\): \(16/2 = 8\), so the 8th observation is \(24\).
- The 9th observation is \(25\).
- Thus, the median is the average of the 8th and 9th observations: \(\frac{24 + 25}{2} = \frac{49}{2} = 24.5\).
Therefore, the median of the given data set is 24.5.
Thus, the correct answer is 24.5, which corresponds to the given option.
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