Complaints about works canteen had been about mess (M) food (F) and se...
Complaints about works canteen had been about mess (M) food (F) and se...
Complaints about the Works Canteen
The complaints about the works canteen can be categorized into three main aspects: mess, food, and service. Let's analyze the given information and determine the number of complainants who had issues with all three aspects.
Given Data:
- Total complaints received: 173
- Number of complaints about mess (M): n(M) = 110
- Number of complaints about food (F): n(F) = 55
- Number of complaints about service (S): n(S) = 6
- Number of complaints about mess and food, but not service: n(M and F, not S) = 20
- Number of complaints about mess and service, but not food: n(M and S, not F) = 11
- Number of complaints about food and service, but not mess: n(F and S, not M) = 16
Determining the Number of Complainants about All Three:
To determine the number of complainants who had issues with all three aspects (mess, food, and service), we need to find the intersection of the three complaint categories.
We can use the principle of inclusion-exclusion to calculate the number of complainants who had issues with all three aspects:
n(M and F and S) = n(M) + n(F) + n(S) - n(M and F, not S) - n(M and S, not F) - n(F and S, not M) + Total Complaints
By substituting the given values:
n(M and F and S) = 110 + 55 + 6 - 20 - 11 - 16 + 173
n(M and F and S) = 197 - 47
n(M and F and S) = 150
Therefore, there were 150 complainants who had issues with all three aspects: mess, food, and service.
Conclusion:
Out of the total 173 complaints received, 150 complainants had issues with all three aspects of the works canteen. This indicates a significant overlap in the complaints, suggesting that the canteen needs to address these concerns comprehensively. By addressing the issues related to mess, food, and service simultaneously, the canteen can work towards improving the overall experience for its users.