Find the median for the following list of values. Give your answer to two decimal places.
8.6, 7.2, 5.1, 12.5, 8.8, 11.8, 12.2, 11.5, 12.1, 13.6
Answer (2)
Sort the list of numbers: 5.1, 7.2, 8.6, 8.8, 11.5, 11.8, 12.1, 12.2, 12.5, 13.6.
Identify the two middle numbers: 11.5 and 11.8.
Calculate the average of the middle numbers: 2 11.5 + 11.8 = 11.65 .
The median is 11.65 .
Explanation
Understanding the Problem We are given a list of 10 numbers and asked to find the median, rounded to two decimal places. The median is the middle value of a sorted list. Since we have an even number of values, the median will be the average of the two middle numbers.
Sorting the Data First, we need to sort the list of numbers in ascending order. The sorted list is: 5.1, 7.2, 8.6, 8.8, 11.5, 11.8, 12.1, 12.2, 12.5, 13.6.
Identifying Middle Numbers Since there are 10 numbers, the two middle numbers are the 5th and 6th numbers in the sorted list. These numbers are 11.5 and 11.8.
Calculating the Median To find the median, we calculate the average of these two numbers: 2 11.5 + 11.8 = 2 23.3 = 11.65
Final Answer The median of the list is 11.65.
Examples
Understanding medians is useful in many real-world scenarios. For example, when analyzing income data, the median income gives a better sense of the 'typical' income than the average income, because it is not as affected by extremely high or low values. Similarly, in sports, the median score can be a more stable measure of a player's performance. In this case, we found the median of a set of numbers, which is a fundamental statistical concept.
The median of the list of values is calculated by sorting the numbers and finding the average of the two middle values. The sorted numbers are: 5.1, 7.2, 8.6, 8.8, 11.5, 11.8, 12.1, 12.2, 12.5, 13.6. The median is 11.65.
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