Given the following data Quantity of Sodas Total Utility Marginal Uti

Given the following data Quantity of Sodas ...

Given the following data $$ \begin{array}{ccc} \begin{array}{c} \text { Quantity of } \\ \text { Sodas } \end{array} & \text { Total Utility } & \text { Marginal Utility } \\ \hline 1 & 20 & - \\ 2 & 25 & ?(\mathrm{a}) \\ 6 & 37 & ?(\mathrm{~b}) \\ \hline \end{array} $$ a. MU between 1 and 2 is__________ b. MU between 2 and 6 is___________

Given the following data
$$
\begin{array}{ccc}
\begin{array}{c}
\text { Quantity of } \\
\text { Sodas }
\end{array} & \text { Total Utility } & \text { Marginal Utility } \\
\hline 1 & 20 & - \\
2 & 25 & ?(\mathrm{a}) \\
6 & 37 & ?(\mathrm{~b}) \\
\hline
\end{array}
$$
a. MU between 1 and 2 is__________
b. MU between 2 and 6 is___________

Key Concepts

Total Utility

Total utility refers to the overall satisfaction or benefit a consumer receives from consuming a certain quantity of goods or services. It is the cumulative measure of utility derived from each unit consumed, and it forms the basis for analyzing changes in consumption and satisfaction.

Marginal Utility

Marginal utility is the additional satisfaction or benefit received from consuming one more unit of a good or service. It is calculated by taking the change in total utility resulting from an increase in consumption and is crucial for understanding consumer choices and the law of diminishing marginal utility.

Discrete Change Calculation

When dealing with non-continuous changes in consumption, the calculation of marginal utility involves determining the difference in total utility between two different levels of consumption and then dividing this change by the difference in quantity. This method is particularly useful when the quantity increases are not uniform.

Transcript

00:01 Hello viewers.

00:02 In this problem we have to explain the idea behind the simpson paradox.

00:06 Now a simpson paradox in statistics is an effect that occurs when a marginal association between any two categorical variable is qualitatively different from the partial association between the same two variables after controlling one or more variables.

00:22 Now in part a of the problem, we have to construct a frequency marginal distribution.

00:27 A marginal distribution of a variable is defined as the frequency distribution of either row or column variable for the desired contingency table respectively.

00:38 It is useful to eradicate the influence of either row or column variable for the desired contingency table.

00:45 Now, we have to add 35, 25 and 20 to obtain the marginal distribution of y1.

00:53 And similarly, we have to add 35 and 65 to obtain.

00:57 The marginal to obtain the corresponding marginal distribution of x1 so adding the corresponding values will give us the frequency marginal distribution table therefore this will be a marginal distribution table where the addition of 35 25 25 20 gives us 80 and the addition of 3565 gives us 100 and the grand total of 80 and 220 gives us 300 so this is part a of a problem now in part b we have to construct a relative frequency marginal distribution so the relative frequency is defined as a number of times the value occurs divided by the total number of observations of in the dataset so it can be written as r f which is the relative frequency so this is frequency divided by total frequency.

01:56 The relative frequency marginal distribution for the row variable is obtained by calculating or dividing the row total for each of the value by the contingency table total.

02:09 That is, for y1 it will be 80 divided by 300.

02:17 Hence, using the same rule, we can construct a table.

02:22 For the frequency marginal distribution.

02:26 Hence, 80 divided by 300 gives us 0 .267, while 220 divided by 300 gives us 0 .77, 733, and so on and so forth...

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