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Rank 1: Same
Rank 2: Same
Rank 3: Same
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Difficulty:
65%
(hard)
Question Stats:
73% (02:45) correct
27%
(03:04)
wrong
based on 1403
sessions
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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.
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.
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 |
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.
| Same | Not same | |
| Rank 1 | ||
| Rank 2 | ||
| Rank 3 |
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Official Answer
Rank 1: Same
Rank 2: Same
Rank 3: Same
16 Apr 2024, 05:44
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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.
(Sort ↕ the table by clicking on the headers)
________________________________________________________________
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 1
Using 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 2
Using 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 3
Using 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
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 |
________________________________________________________________
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 1
Using 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 2
Using 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 3
Using 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
08 Dec 2024, 14:07
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This question is so simple once you figure out what it's actually trying to ask you. Took me like 3.5 minutes to even understand what it was saying...
