MHB Calculating Median in a Class with B, D, A, and C Scores: Findings and Solutions

  • Thread starter Thread starter Monoxdifly
  • Start date Start date
  • Tags Tags
    Median
AI Thread Summary
In the discussion about calculating the median of scores for students Budi, Doni, Adi, and Coki, it is established that Budi's score is greater than Doni's, and the sum of Adi's and Doni's scores exceeds that of Budi's and Coki's. The inequalities suggest that the scores can be arranged in two possible orders, but a definitive median cannot be calculated due to insufficient information. The analysis indicates that if C's score is between B and A or between D and B, the median would be the average of B and C or B and D, respectively. Ultimately, the median can be expressed as half of the sum of B and the maximum of C or D. It is concluded that determining an exact median value is not feasible with the given data.
Monoxdifly
MHB
Messages
288
Reaction score
0
In a class, Budi's score is greater than Doni's. The sum of Adi's and Doni's scores is greater than the sum of Budi's and Coki's scores. Meanwhile, Doni's score is greater than two times Budi's score substracted by Adi's score. Determine the median of those four students' scores.

All I know, was, by using their initials that:
B > D
A + D > B + C
D > 2B - A

And by using the second and third info I got that their score from lowest to highest is either C, D, B, A or D, B, C, A. However, I met a dead-end after that. Please someone help me.
 
Mathematics news on Phys.org
I sketched a number line ... $B>D$ is obvious. The last inequality states $B < \dfrac{A+D}{2}$, or $B$ is less than the average of $A$ and $D$, equal to the midpoint of segment $AD$.

Finally, the second inequality states $C < A+D-B$. Note the possible positions for $C$ represented by the open-ended blue ray in the diagram.

If $B < C< A$ or $D < C < B$, the the median of the four scores is $\dfrac{B+C}{2}$

If $C < D$, then the median is $\dfrac{B+D}{2}$
 
Yep. Put more concisely, the median is $\frac 12 (B+\max(C,D))$.
 
Thank you everyone who has helped me with this question. I have asked this question in 4 different forums including this one and all confirm that it is impossible to find the exact number of the median's value.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top