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Example: Find the median of the following numbers. a) 6, 5, 2, 8, 9, 4. b) 2, 1, 8, 3, 5, 8.
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2 partsStep-by-step solution
10 stepsThe problem asks us to find the median for two sets of numbers.
Part a· 5 steps
The numbers are: 2, 6, 5, 8, 9, 4.
Arrange the numbers in ascending order.
Count the total number of values ().
There are 6 numbers in the set, so .
Determine the position of the median.
Since is an even number, the median is the average of the two middle values. These are the values at positions and .
The positions are and .
So, we need to find the 3rd and 4th values in the ordered list.Identify the 3rd and 4th values.
The ordered list is: 2, 4, 5, 6, 8, 9
The 3rd value is 5.
The 4th value is 6.Calculate the median.
The median is the average of the 3rd and 4th values.
The median for part a) is .
Part b
The numbers are: 1, 2, 8, 3, 5, 8.
Arrange the numbers in ascending order.
Count the total number of values ().
There are 6 numbers in the set, so .
Determine the position of the median.
Since is an even number, the median is the average of the two middle values. These are the values at positions and .
The positions are and .
So, we need to find the 3rd and 4th values in the ordered list.Identify the 3rd and 4th values.
The ordered list is: 1, 2, 3, 5, 8, 8
The 3rd value is 3.
The 4th value is 5.Calculate the median.
The median is the average of the 3rd and 4th values.
The median for part b) is .
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