3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers k ≠m, what is the median of the list?
A. 2
B. 2.5
C. 3
D. 3.5
D. 4
The OA is C.
Hi, I need some help,
List = {2,3,3,8,k,m}
Given that mean is more than 4
which implies 2+3+3+ 8+ k+m >4*6 --> k+m> 8
and we know k ≠m,
therefore
k=1, m=8 median = 3 { 1,2,3,3,8,8}
k=5, m =10 median = 4 {2,3,3,5,8,10}
Thanks in advance!
The arithmetic mean of the list of numbers
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The arithmetic mean of the list of numbers above is 4.AAPL wrote:3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers k ≠m, what is the median of the list?
A. 2
B. 2.5
C. 3
D. 3.5
D. 4
So, (3 + k + 2 + 8 + m + 3)/6 = 4
Multiply both sides by 6 to get: 3 + k + 2 + 8 + m + 3 = 24
Simplify: 16 + k + m = 24
Subtract 16 from both sides to get: k + m = 8
If k and m are integers k ≠m, what is the median of the list?
Let's assign some values to k and m that satisfy the above condition AND such that k + m = 8
How about k = 1 and m = 7
So, our set of values becomes {3, 1, 2, 8, 7, 3}
What is the median of the list?
Arrange numbers in ASCENDING ORDER to get: { 1, 2, 3, 3, 7, 8}
Since we have an EVEN number of values, the median will equal the AVERAGE of the 2 middlemost values
Median = (3 + 3)/2 = 6/2 = 3
Answer: C
Cheers,
Brent
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Using the average formula: average = sum/number, we see that the sum of these numbers is 24. Thus we have:AAPL wrote:3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers k ≠m, what is the median of the list?
A. 2
B. 2.5
C. 3
D. 3.5
D. 4
3 + k + 2 + 8 + m + 3 = 24
16 + k + m = 24
k + m = 8
Since k ≠m and assuming that k < m, then the ordered pairs of (k, m) could be (3, 5), (2, 6), (1, 7), (0, 8), etc.
Let's investigate the possible ordered pairs further:
If (k, m) = (3, 5), then the numbers in ascending order are:
2, 3, 3, 3, 5, 8 --- with median = 3
If (k, m) = (2, 6), then the numbers in ascending order are:
2, 2, 3, 3, 6, 8 --- with median = 3
If (k, m) = (1, 7), then the numbers in ascending order are:
1, 2, 3, 3, 7, 8 --- with median = 3
If (k, m) = (0, 8), then the numbers in ascending order are:
0, 2, 3, 3, 8, 8 --- with median = 3
At this point, we can see that no matter how we "stretch" k and m (e.g., let's say (k, m) = (-92, 100)), we would still have median = 3.
Answer: C
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