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In a two-way frequency table, the marginal frequencies is the 'total' entry for the row and the 'total' entry for the column
The result of the data organized in a two way table with the marginal frequency included is as follows;
[tex]\begin{array}{|l|c|c|c|}\mathbf{\underline{Device \ Student \ Use}}&\mathbf{\underline{Laptop}}&\mathbf{\underline{Do\ not \ use \ laptop}}&\mathbf{\underline{Total}}\\&&&\\\mathbf{Tablet}&49 &75&\underline{124}\\&&&\\\mathbf{Do\ not \ use \ tablet}&63&97&\underline{160}\\&&&\\\mathbf{Total}&\underline{112}&\underline{172}&284\\&&&\end{array}[/tex]
The reason the above table is correct is as follows:
The known parameters are;
Number of students in the survey, U = 284 students
The number of students that use a laptop, n(L) = 112
The number of students that also use a tablet, T ∩ L = 49
The number of students that do not use a laptop or a tablet, [tex]n(T \cup L)^c[/tex] Â = 97
Required:
To organize the result of the survey in a two-way table
Solution:
U = [tex]n(T \cup L)^c[/tex] + n(T ∪ L)
Therefore;
n(T ∪ L) = U - [tex]n(T \cup L)^c[/tex]
n(T ∪ L) = 284 - 97 = 187
n(T ∪ L) = 187
The number of students that use only a laptop = n(L) - n(T ∩  L) = 112 - 49 = 63
The number of students that use only a laptop [n(L) - n(T ∩  L)] = 63
n(T ∪ L) = n(T) + n(L) - n(T ∩ L)
n(T) = n(T ∪ L) - [n(L) - n(T ∩ L)]
n(T) = 187 - 63 = 124
The number of students that use only tablets = n(T) - n(T ∩  L) = 124 - 49 = 75
The number of students that use only tablets, [n(T) - n(T ∩  L)] = 75
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The results are organized in the attached two way table and the marginal frequencies are the numbers underlined in the totals column
[tex]\begin{array}{|l|c|c|c|}\mathbf{\underline{Device \ Student \ Use}}&\mathbf{\underline{Laptop}}&\mathbf{\underline{Do\ not \ use \ laptop}}&\mathbf{\underline{Total}}\\&&&\\\mathbf{Tablet}&49 &75&\underline{124}\\&&&\\\mathbf{Do\ not \ use \ tablet}&63&97&\underline{160}\\&&&\\\mathbf{Total}&\underline{112}&\underline{172}&284\\&&&\end{array}[/tex]
Learn more about marginal frequencies here:
https://brainly.com/question/16401512
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