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For each of the following sets find the median.a 2, 2, 4, 6, 7, 9 b 1, 1, 2, 9, 9, 10c 1, 3, 5, 7, 8, 10, 13, 14 d 0, 1, 9, 13, 1, 10, 7, 12, 9, 2

Question

For each of the following sets find the median.a 2, 2, 4, 6, 7, 9 b 1, 1, 2, 9, 9, 10c 1, 3, 5, 7, 8, 10, 13, 14 d 0, 1, 9, 13, 1, 10, 7, 12, 9, 2

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Solution

Sure, let's find the median for each set.

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. If there is an even number of observations, the median will be the average of the two middle numbers.

a) 2, 2, 4, 6, 7, 9 First, we need to sort the numbers in ascending order, but they are already sorted. Since there are 6 numbers, we take the average of the 3rd and 4th numbers. Median = (4 + 6) / 2 = 5

b) 1, 1, 2, 9, 9, 10 The numbers are already sorted. Since there are 6 numbers, we take the average of the 3rd and 4th numbers. Median = (2 + 9) / 2 = 5.5

c) 1, 3, 5, 7, 8, 10, 13, 14 The numbers are already sorted. Since there are 8 numbers, we take the average of the 4th and 5th numbers. Median = (7 + 8) / 2 = 7.5

d) 0, 1, 9, 13, 1, 10, 7, 12, 9, 2 First, we need to sort the numbers in ascending order: 0, 1, 1, 2, 7, 9, 9, 10, 12, 13. Since there are 10 numbers, we take the average of the 5th and 6th numbers. Median = (7 + 9) / 2 = 8

So, the medians for the sets are 5, 5.5, 7.5, and 8 respectively.

This problem has been solved

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