In a music contest, a panel of 100 audience members ranked each of 4 performers with integer ranks—from 1 to 4. For each performer, the table indicates the number of audience members who assigned each rank to the given performer. For example, exactly 49 audience members assigned rank 4 to Performer A. Two methods—the Mode Method and the Median Method—are used to assign final ranks to the performers based on these audience rankings.
Mode Method: Assign to each performer a final rank equal to the audience rank the performer received most often.
Median Method: Compute the median audience ranking for each performer. The ordering of the final rankings will be the same as the ordering of these medians.
| Rank |
Performer | 1 | 2 | 3 | 4 |
---|
A | 51 | 0 | 0 | 49 |
B | 23 | 5 | 72 | 0 |
C | 5 | 95 | 0 | 0 |
D | 21 | 0 | 28 | 51 |
|
(Sort ↕ the table by clicking on the headers)
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For each of the following final ranks, select Same if the two final ranking methods assigned the same performer the given rank. Otherwise, select Not same.Rank 1Using the mode method for Rank 1, we see that the only performer who received Rank 1 most often was Performer A, who received Rank 1 from 51 audience members.
Also, the median ranking for Performer A was Rank 1 since over half of Performer A's rankings were Rank 1, so the middle ranking for Performer A was Rank 1. Also, no other performer had a median ranking of Rank 1.
So, Performer A was assigned Rank 1 both ways.
Select
Same.
Rank 2Using the mode method for Rank 2, we see that the only performer who received Rank 2 most often was Performer C, who received Rank 2 from 95 audience members.
Also, the median ranking for Performer C was Rank 2 since over half of Performer C's rankings were Rank 2, so the middle ranking for Performer C was Rank 2. Also, no other performer had a median ranking of Rank 2.
So, Performer C was assigned Rank 2 both ways.
Select
Same.
Rank 3Using the mode method for Rank 3, we see that the only performer who received Rank 3 most often was Performer B, who received Rank 3 from 7 2 audience members.
Also, the median ranking for Performer B was Rank 3 since over half of Performer B's rankings were Rank 3, so the middle ranking for Performer B was Rank 3. Also, no other performer had a median ranking of Rank 3.
So, Performer B was assigned Rank 3 both ways.
Select
Same.
Correct answer: Same,
Same,
Same