The following list has a median of 43. What would be the new median if 21 was added to the list??
The list is: 31, 48, 50, 23, 28, 52, 57, 38, 56, 27
arranging the list in order ... 23, 27, 28, 31, 38, 48, 50, 52, 56, 57
the list has an even number of entries
... so the median is the average of the two middle values ... 38 and 48
adding 21 to the list gives the list an odd number of entries
... the middle value in the list is the median ... 38
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Well, well, well, looks like we're going to shake things up in this list! Adding 21 would definitely mix things up. Now, to find the new median, we need to remember that the median is the middle value when the list is sorted.
Let's add 21 to the list: 31, 48, 50, 23, 28, 52, 57, 38, 56, 27, 21.
Now, we'll sort the list in ascending order: 21, 23, 27, 28, 31, 38, 48, 50, 52, 56, 57.
Counting the numbers from left to right, we find the middle value is 31. Oh boy, it seems like the median stayed the same despite our attempts to shake things up! So, the new median is still 31.
The joke's on us! No matter how much we try to change things, sometimes they just stay the same.
To find the median of a list, you need to first arrange the numbers in ascending order.
The given list in ascending order is:
23, 27, 28, 31, 38, 48, 50, 52, 56, 57.
Now, we can find the current median. Since there are 10 numbers in the list, the middle two numbers are 38 and 48. The median is the value halfway between these two numbers.
So, the current median is (38 + 48) / 2 = 43.
To find the new median if 21 is added to the list, we need to add 21 to the appropriate position in the sorted list. Since the list is already in ascending order, we can insert 21 in its correct position.
The updated list with 21 added in the correct position is:
21, 23, 27, 28, 31, 38, 48, 50, 52, 56, 57.
Now, let's find the new median. Since there are 11 numbers in the list, the middle number is at position (11 + 1) / 2 = 6th position.
So, the new median is the value at the 6th position, which is 38.
Therefore, the new median after adding 21 to the list would be 38.