Answer :
Final Answer:
Adding a value of 60 degrees to the data would cause the median to increase to 79.5 degrees.
Explanation:
When calculating the median, we arrange the data in ascending order: 57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105. The median is the middle value in this sorted sequence, which is 82 degrees.
If we add a value of 60 degrees to the data, the new sequence becomes: 57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105. Now, the middle two values are 77 and 82, and the average of these two values is (77 + 82) / 2 = 79.5 degrees, which becomes the new median.
In summary, the median temperature increases from 82 degrees to 79.5 degrees when a value of 60 degrees is added to the data.
In statistics, the median is a measure of central tendency that represents the middle value in a data set when it's arranged in ascending or descending order. It's less sensitive to outliers compared to the mean, making it a useful indicator of the data's central location. When working with data sets that have an odd number of values, the median is the middle value.
However, when dealing with data sets with an even number of values, the median is the average of the two middle values. Understanding the median is important for analyzing data and drawing accurate conclusions, particularly when the distribution is not symmetrical or when outliers can significantly affect the mean. It's a valuable tool in various fields such as economics, biology, and social sciences.
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