Solve the data set.

Question

Solve the data set.

 

                                Male                        Female

 

Upper class                  12                              8

working class                23                            40

 

1. what percentage of the class is a member of the upper class?

2. what is the proportion of females that belong to the working class?

3. what is the ratio between the upper and working classes?

4. what is the formula for computing the mean?

 

 

Answer 1

1. The percentage of members that are also members of the upper class

is found by finding the total number of members who are in the upper

class and dividing by the total number of members.

 

I am going to assume that a member cannot be both in the upper class

as well as the working class, otherwise, based only on the information you

gave, it would not be possible to determine the total number of members.

 

So the total number of members is 12 + 8 + 23 + 40 = 83

 

# of members of the upper class = 12 + 8 = 20

 

% of members of the upper class out of the total members = 20/83 * 100% = 24.10 % (approximately)

 

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2. the proportion of females that belong to the working class can be answered

differently depending on how you interpret the question itself.

 

If we assume that the question is asking what proportion of females out of the total number

of females belong to the working class then the proportion is 40/48, where 48 is the total

number of females.

 

If we instead assume the question is asking for the proportion of females that are in the

upper class out of the total number of members (both male and female) then it would

be 40/83 (because 83 is the total number of members.

 

Proportions are defined as fractions, so in order to express a proportion of 'x number of things' to 'y number of things' you simply place it as x/y. In some cases you may have to calculate either x or y's values, just as

we did when answering the first question.

 

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3. a ratio is similar to a proportion except that we express it as a:b, if for example we wanted the ratio of 'a to b'

So, to express the ratio of upper class to working class we find the value of each first: upper class = 12 + 8 = 20

and working class is 23 + 40 = 63.

So the ratio of upper to working class is 20 : 63

 

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4. To be honest with you, I'm not completely certain what is meant by the question 'what is the formula for computing the mean,' in this context.

 

Generally to compute a mean, you would have a set of values that you add up and divide by the total number of values. For example if you want to calculate the mean for the number 5, 5, 7, and 3, you would do the following:

 

(5 + 5 + 7 + 3) / 4 = 20 / 5 = 4, so 4 is the mean of 5, 5, 7, and 3.

 

the formula could be expressed as: ∑x_i / n , where i = 1 to n , and n is the number of values for which you are calculating the mean. Its a fancy way to say "sum up the numbers and divide by the total number of things you summed up".

 

That formula can be written a little easier, however the formatting options on this forum are somewhat limited when it comes to mathematical expressions.