To find out how the median changes when the number 29 is added to the original set of numbers, we first need to determine the median of the initial set of numbers.
The original set is: 71308220561474873211
This set contains 20 digits. We can treat each digit as a number. To find the median of a set with an even number of elements, we need to arrange the elements in order and then take the average of the two middle numbers.
First, let's separate out the individual digits and sort them:
Digits: 1, 1, 2, 2, 3, 4, 5, 6, 7, 7, 8, 0, 8, 1, 3, 2, 0, 2, 5, 6
Now let's sort them: 0, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8
Now we find the median. Since there are 20 numbers (even count), the median will be the average of the 10th and 11th numbers in the sorted list.
From the sorted list:
- The 10th number is 5.
- The 11th number is 6.
Median of the original set: \[ \text{Median} = \frac{5 + 6}{2} = 5.5 \]
Next, we add the number 29 to the set. This means we now have a new set of 21 numbers (20 original digits + 1 additional number).
We need to find the new median. First, we include the new number and then re-sort the digits combined:
New set of digits (including 29): 0, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 2, 9 (added 9 for 29)
We sort these numbers: 0, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 2
Now since the count of numbers is odd (21), the median will be the middle number, which will be the 11th number in the sorted list.
New median:
- The sorted list is: 0, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9
- The 11th number is 6.
Thus, the new median is 6.
Therefore, the median changes from 5.5 to 6 when the number 29 is added to the set.
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