How can one calculate median ?1 - Arrange the elements of the data set in an ascending or descending order without skipping any element.
2 - Check if the number of elements in the set are ODD or EVEN.
3 - If ODD, Median = the middle element of the arranged set.
If EVEN, Median = Average of the 2 middle elements.
Things we know here -1. Each team has 3 participants in the test.
2. Alex's score is the median score of all participants.
3. Bob's score < Alex's score.
4. Bob's rank amongst all participants is 19.
5. Cathy's rank amongst all participants is 28
Now, let us look at the options.
Option 1: 6
Number of teams: 6
Number of participants: 6*3 = 18
We can reject this option because we know Bob's rank is 19 and Cathy's rank is 28 which are beyond number of participants as per this option.
A = Wrong.Option 2: 9
Number of teams: 9
Number of participants: 9*3 = 27
We can reject this option because we know Cathy's rank is 28 which is beyond number of participants as per this option.
B = Wrong.Option 3: 10
Number of teams: 10
Number of participants: 10*3 = 30
Arrangement of scores of 30 participants can be: 14 scores -- 15th score -- 16th score -- 14 more scores
As per formula for median, Alex's score would be an average of the 15th and 16th score but that would increase the number of scores then by 1 making it 31 scores which is not correct as per the option. Hence,
C = Wrong.Option 4: 11
Number of teams: 11
Number of participants: 11*3 = 33
Arrangement of scores of 33 participants can be: 16 scores -- 16th score -- 16 more scores
This holds true with all the given information. Hence,
D = Correct.Option 5: 13
Number of teams: 13
Number of participants: 13*3 = 39
Arrangement of scores of 39 participants can be: 19 scores -- 20th score -- 19 more scores
Here, this does not hold true with the information given as we know Bob's rank is 19th and that Alex's score is greater than Bob's but we know Alex's score is the median of all participants and hence is the 20th score. This is an anomaly because as per ranks, Alex's rank should be less than Bob's which is not holding true. Hence,
E = Wrong.----
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