The median of $9, 5, 7, 11, 13, 3$ is...
a) 7
b) 8
c) 9
d) 11
Answer (2)
Arrange the data in ascending order: 3 , 5 , 7 , 9 , 11 , 13 .
Identify the two middle values since there are an even number of data points: 7 and 9 .
Calculate the average of the two middle values: 2 7 + 9 = 8 .
The median of the data set is 8 .
Explanation
Understanding the Median We are given the data set 9 , 5 , 7 , 11 , 13 , 3 and asked to find the median. The median is the middle value of a data set when the data is arranged in ascending order. If there is an even number of data points, the median is the average of the two middle values.
Arranging the Data First, we need to arrange the data set in ascending order: 3 , 5 , 7 , 9 , 11 , 13 .
Identifying Middle Values Since there are 6 numbers in the data set, which is an even number, the median is the average of the two middle values. The two middle values are the 3rd and 4th numbers, which are 7 and 9.
Calculating the Average Now, we calculate the average of 7 and 9: 2 7 + 9 = 2 16 = 8 .
Final Answer Therefore, the median of the data set 9 , 5 , 7 , 11 , 13 , 3 is 8.
Examples
The median is a useful measure in real life when you want to find the 'middle' value of a set of data, especially when the data might have outliers (extreme values). For example, if you want to know the typical income in a neighborhood, the median income is often more informative than the average income because it is not as affected by a few very high or very low incomes. If the incomes in a neighborhood are $20,000, $30,000, $40,000, $50,000, and $1,000,000, the average income is $228,000, which doesn't really represent the typical income. The median income, however, is $40,000, which is a much better representation of the typical income.
To find the median of the dataset 9 , 5 , 7 , 11 , 13 , 3 , we arranged the numbers in ascending order to get 3 , 5 , 7 , 9 , 11 , 13 . The two middle values, 7 and 9 , average to 8 , making the median 8 . Therefore, the answer is b) 8 .
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