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Your calculation for the mean and standard deviation for the set 1,2,3,4,5,6 is correct, but I do not think that is what you are asked to do. Let me try to guess the problem from your table:
You are given that a group of people are asked the number of cups of coffee that they drink in the morning; the results are presented in the table. I.e. 32 people drank 1 cup, 9 people drank 2 cups, etc...
I'm not sure what you are asked to find. The number of cups for the top 10%? Bottom 10%? Number of cups on average with a 90% confidence level? The range of number of cups that encompasses 90% of the population?
In any case, what you have is a weighted mean -- you have to take into account the weights.
In order to find the weighted mean, you multiply each frequency by its corresponding weight, and then divide by the total weights.
Here you get `bar(x)=(1(32)+2(9)+3(3)+4(3)+5(2)+6(14))/(32+9+3+3+2+14)=165/63~~2.619`
Thus the "average" person drank 2.6 cups.
The standard deviation is 2.0668 if this is a sample, and 2.0503 if this is the population.
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