Points to Remember:
- Median is the middle value in a dataset when arranged in ascending or descending order.
- For an even number of data points, the median is the average of the two middle values.
Introduction:
The question requires finding the median of a given dataset. The median is a measure of central tendency, providing a value that represents the “middle” of a dataset. Unlike the mean (average), the median is less sensitive to outliers (extremely high or low values) that can skew the mean. This makes the median a useful statistic when dealing with data that might contain such outliers.
Body:
1. Arranging the Data:
To find the median, we first need to arrange the data in ascending order:
12, 21, 27, 34, 34, 34, 43, 49, 50, 50
2. Identifying the Median:
Since there are 10 data points (an even number), the median will be the average of the two middle values. The two middle values are the 5th and 6th values in the ordered dataset: 34 and 34.
3. Calculating the Median:
The median is calculated as:
(34 + 34) / 2 = 34
Therefore, the median of the given dataset is 34.
Conclusion:
In summary, the median of the dataset {34, 49, 50, 34, 21, 27, 50, 34, 12, 43} is 34. This value provides a robust representation of the central tendency of the data, less susceptible to distortion by extreme values compared to the mean. Understanding and applying the concept of the median is crucial for accurate data analysis across various fields, from statistics and economics to social sciences and environmental studies. The ability to correctly calculate the median ensures a more reliable and representative understanding of the data being analyzed, promoting better decision-making based on factual information.