1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harman [31]
3 years ago
6

There is another way to rank the difficulty of test questions using Networks: Each student gives scores for each problem, then w

e construct a network whose nodes/vertices are the problems of the exam. There is an arc from problem A to B for student k that did better in problem B than in problem A, (i.e., if sA, sB are the scores of those problems, sB > sA). The weight of the arc yk associated to student k equals (approximately) the difference of score the student received in those two problems sB −sA = yk. Explain why the Massey’s method we saw in class can be used for rating exam problems by difficulty.
Mathematics
1 answer:
Vlad [161]3 years ago
7 0

Answer:

Step-by-step explanation:

Truly, on a single student level, the Massey method can be applied i.e. problems are ranked according to their level of difficulty for a single student.

Let us say there are 4 problems P1, P2, P3, P4 set in an exam where a student has to solve any two.

Assuming student 1 solves and scores more in P1 than in P2, r1>r2

student 2  more in P1 than P4 r1>r4

student 3 more in P2 than P4 r2>r4

student 4 more in P4 than P3 r4>r3

student 5 more in P2 than P3 r2>r3

and such many more cases.

then the Massey's model can be written as

P1 P2 P3  P4

\begin{bmatrix} 1 &-1 &0 &0\\ 1 &-1 &0 &0 \\ 0 &1 & 0 &-1 \\ 0 & 0 &-1 & 1 \\ 0 & 1 & -1 & 0 \end{bmatrix}.

\times \begin{bmatrix}r1 \\r2 \\r3 \\r4 \end{bmatrix}  =

\begin{bmatrix}y_{1} \\ y_{2} \\ y_{3} \\ y_{4}\\ y_{5}\end{bmatrix}.            

If Pi gives more score than Pj, the entry below Pi shall be 1 and below Pj shall be -1.

The rest of the entries shall be 0.

r1,r2,r3,r4,r5 are ranks .  

There may be more rows depending upon more combination of 2 problems.

Should in case more than one student solve the same combination and get scores in the same order, for instance, 12 students solve P1 and P2, for 7 of them r1>r2, then their scores can be averaged.

Normally, such systems are overdetermined, i.e., more rows than the number of unknowns, then it is solved by the Least square method ., as there shall be no a solution with least error is found out.

The overall ranking, in reverse order, shall give the ranking according to increasing difficulty.

You might be interested in
Simplify the following
Lady_Fox [76]
Your answer is right

3 0
4 years ago
WHAT ARE THE THREE DIFFERENT TYPES OF ANGLES!!!!!!??
Vikentia [17]
<em>Hello there, and thank you for asking your question here on brainly.

<u>Answer: The three different types of angles are an acute angle, which is an angle that is an angle that measures from 1</u></em>° <em><u>to 89°. A right angle, that specifically measures to 90</u></em>°. <em><u>Finally, an obtuse angle that measures from 91° to 179°. An angle that also measures 180° is a straight line, and is called a straight angle. 

</u>Hope this helped you! ♥<u>
</u></em>
6 0
3 years ago
3. Kevin weighs 57 kilograms (kg) and his father weighs 85 kg. How much less
Lelu [443]

Answer:

his father weighs 28 kg more :)

4 0
3 years ago
A store advertises that it is offering a 14% discount on all articles purchased at the store. if yao pays $670.80 for an article,
gizmo_the_mogwai [7]
The answer is <span>$576.888</span>
8 0
3 years ago
What is 9 5/6 - 2 1/3
Mariana [72]
9 5/6 - 2 1/3 is 7 1/2.

You could get this answer by finding the same denominator of the fractions. The LCM of both is 6. Multiply the 1 of the second fraction 2 times because you had to multiply the denominator 2 times to get to 6. 
You should have 2 2/6.

Now get 9 5/6 - 2 2/6.

The answer is 7 3/6, simplifies into 7 1/2.
9 5/6 - 2 1/3 is 7 1/2.


5 0
3 years ago
Read 2 more answers
Other questions:
  • I need help on this worksheet for my math hw it’s combing like terms?
    6·1 answer
  • will ate a snack with 68.44 total calories.If the chip he ate were 39.94 calories, how many calories were in the rest of his sna
    5·1 answer
  • In a certain town, 30% of the people are Conservatives; 50% Socialists; and 20% Liberals. In this town at the last election, 65%
    13·1 answer
  • Equilateral of triangle
    12·1 answer
  • One number is seven more than three times another number. If the sum of the numbers is 15, find the numbers.
    13·1 answer
  • Suppose you cut a small square from a square of fabric as shown in the diagram. Write
    5·1 answer
  • Solve the equation 4x +30 = 2(x-10)
    12·1 answer
  • What is the highest degree in x³ - x²y² - y² + 2​
    7·1 answer
  • What would the correct word form be for the number 382
    12·2 answers
  • A deep sea diver descends from the surface of the ocean at a rate of 33 feet per minute.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!