Answer :
To determine how much the median would increase when the number 5 is added to the given set of numbers [tex]\(\{6, 2, 2, 4, 6, 7\}\)[/tex], we need to follow these steps:
1. Sort the original set of numbers.
2. Find the median of the original set.
3. Add the number 5 to the set and sort the new set.
4. Find the median of the new set.
5. Calculate the increase in the median.
### Step 1: Sort the Original Set
The original set is: [tex]\(\{6, 2, 2, 4, 6, 7\}\)[/tex].
Sorting these numbers in ascending order:
[tex]\[ \{2, 2, 4, 6, 6, 7\} \][/tex]
### Step 2: Find the Median of the Original Set
To find the median of a set with an even number of elements (6 elements in this case), we take the average of the two middle numbers.
The sorted set is [tex]\(\{2, 2, 4, 6, 6, 7\}\)[/tex].
The two middle numbers are the third and fourth numbers in this sorted list: 4 and 6.
So, the median of the original set is:
[tex]\[ \text{Median} = \frac{4 + 6}{2} = \frac{10}{2} = 5 \][/tex]
### Step 3: Add the Number 5 and Sort the New Set
The new set is: [tex]\(\{6, 2, 2, 4, 6, 7, 5\}\)[/tex].
Sorting the new set in ascending order:
[tex]\[ \{2, 2, 4, 5, 6, 6, 7\} \][/tex]
### Step 4: Find the Median of the New Set
To find the median of a set with an odd number of elements (7 elements in this case), we take the middle number.
The sorted new set is [tex]\(\{2, 2, 4, 5, 6, 6, 7\}\)[/tex].
The middle number is the fourth number in this sorted list: 5.
So, the median of the new set is:
[tex]\[ \text{Median} = 5 \][/tex]
### Step 5: Calculate the Increase in the Median
Now, we compare the medians of the original and new sets.
- Median of the original set: [tex]\( 5 \)[/tex]
- Median of the new set: [tex]\( 5 \)[/tex]
The increase in the median is:
[tex]\[ \text{Increase} = 5 - 5 = 0 \][/tex]
Therefore, the median would remain the same and the increase in the median would be [tex]\(0\)[/tex].
1. Sort the original set of numbers.
2. Find the median of the original set.
3. Add the number 5 to the set and sort the new set.
4. Find the median of the new set.
5. Calculate the increase in the median.
### Step 1: Sort the Original Set
The original set is: [tex]\(\{6, 2, 2, 4, 6, 7\}\)[/tex].
Sorting these numbers in ascending order:
[tex]\[ \{2, 2, 4, 6, 6, 7\} \][/tex]
### Step 2: Find the Median of the Original Set
To find the median of a set with an even number of elements (6 elements in this case), we take the average of the two middle numbers.
The sorted set is [tex]\(\{2, 2, 4, 6, 6, 7\}\)[/tex].
The two middle numbers are the third and fourth numbers in this sorted list: 4 and 6.
So, the median of the original set is:
[tex]\[ \text{Median} = \frac{4 + 6}{2} = \frac{10}{2} = 5 \][/tex]
### Step 3: Add the Number 5 and Sort the New Set
The new set is: [tex]\(\{6, 2, 2, 4, 6, 7, 5\}\)[/tex].
Sorting the new set in ascending order:
[tex]\[ \{2, 2, 4, 5, 6, 6, 7\} \][/tex]
### Step 4: Find the Median of the New Set
To find the median of a set with an odd number of elements (7 elements in this case), we take the middle number.
The sorted new set is [tex]\(\{2, 2, 4, 5, 6, 6, 7\}\)[/tex].
The middle number is the fourth number in this sorted list: 5.
So, the median of the new set is:
[tex]\[ \text{Median} = 5 \][/tex]
### Step 5: Calculate the Increase in the Median
Now, we compare the medians of the original and new sets.
- Median of the original set: [tex]\( 5 \)[/tex]
- Median of the new set: [tex]\( 5 \)[/tex]
The increase in the median is:
[tex]\[ \text{Increase} = 5 - 5 = 0 \][/tex]
Therefore, the median would remain the same and the increase in the median would be [tex]\(0\)[/tex].
It wouldn’t increase because 5 is not the highest nor the lowest number of the set
