Instructions

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.

Solution

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

orÂ

S: 3,3,3,~~4,4,~~4,5,5,6,7

F:Â ~~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 2Â 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 becauseÂ "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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