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Simple Happiness index (SHI) of a country is computed on the basis of three, parameters: social support (S),freedom to life choices (F) and corruption perception (C). Each of these three parameters is measured on a scale of 0 to 8 (integers only). A country is then categorised based on the total score obtained by summing the scores of all the three parameters, as shown in the following table:
Following diagram depicts the frequency distribution of the scores in S, F and C of 10 countries - Amda, Benga, Calla, Delma, Eppa, Varsa, Wanna, Xanda,Yanga and Zooma:
Further, the following are known.
1. Amda and Calla jointly have the lowest total score, 7, with identical scores in all the three parameters.
2. Zooma has a total score of 17.
3. All the 3 countries, which are categorised as happy, have the highest score ln exactly one parameter.
The frequency distribution is:
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
or
S: 3,3,3,4,4,4,5,5,6,7
F: 1,1,2,3,3,4,5,5,5,7
C: 1,2,2,2,3,3,3,3,4,6
Zooma(Z) has a total score of 17 (comes under happy category), and other 2 countries, which are categorized as happy, have the highest score in exactly one parameter.
Suppose the other two countries are P and Q
Z have two possibilities for S, F, C : (6,7,4) & (6,5,6)
All the other cases are negated because "All the 3 countries, which are categorised as happy, have the highest score ln exactly one parameter."
For Example : 7,7,3 is not possible because 7 being the highest score is there in two parameters.
So, it scored 6 in S in both the cases.
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