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
A Pizza factory has come out with two kinds of pizzas.A square pizza of side 26 cm costs AED 80 and a circular pizza of diameter
DiKsa [7]

Answer:

Square pizza

Step-by-step explanation:

To obtain which pizza is the best buy:

Cost of square pizza :

AED 80

side length, s = 26cm

Area of square, A = s²

A = 26² = 676 cm²

1 AED of square pizza gives : 676 / 80 = 8.45 cm²

Cost of circular pizza :

AED 80

Radius, r = 28cm

Area of circle, A = πr²

A = 22/7 * 14 * 14 = 22 * 2 * 14 = 616 cm²

1 AED of circular pizza gives : 616 / 80 = 7.7cm²

Hence, square pizza is the better buy ;

8.45cm² > 7.70 cm²

4 0
3 years ago
In 1993 the federal government boosted income tax rates. The change in tax revenue that
worty [1.4K]

Answer: D. contradicted the claims of supply-side economists and the Laffer Curve

Step-by-step explanation: In 1993 the federal government boosted income tax rates. The change in tax revenue that occurred in the seven years that followed: contradicted the claims of supply-side economists and the Laffer Curve.

7 0
3 years ago
Pls help 6th grade math
Rasek [7]

Answer:

60% of 500 is 300 and 40% of 500 is 200. 300-200=100

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I NEED HELP WITH THIS ASAP <br> I WILL GIVE BRAINLIEST
natita [175]

Answer

x=100

y= 4.5

x=6

y= 1.87

Step-by-step explanation:

4 0
2 years ago
I'm not sure how to do this. Help please?
OLEGan [10]
The area is 65 m squared
7 0
3 years ago
Other questions:
  • The function below describes the number of students who enrolled at a university, where f(t) represents the number of students a
    11·1 answer
  • What is -4+4 showing additive inverse
    15·1 answer
  • What percent of 600 is 12
    8·1 answer
  • Q)READ THE CLUES TO FIND THE MYSTERY NUMBER.
    11·1 answer
  • Whats the circumference of a circle if the radius is 4.6
    11·1 answer
  • What is the area of a triangle whose vertices are J(−2, 1) , K(4, 3) , and L(−2, −5) ?
    10·1 answer
  • Please help me out :))
    11·1 answer
  • WILL GIVE BRAINLIEST AND 5 STARS PLEASE HURRY! y= ____ x= ____
    6·1 answer
  • Find the measure of x
    5·1 answer
  • What is the approximate value of √8
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!