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In a <em>two-way frequency table</em>, 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 <u>two way table</u> with the <u>marginal frequency</u> included is as follows;
The reason the above table is correct is as follows:
The known parameters are;
Number of students in the survey, <em>U</em> = 284 students
The number of students that use a laptop, <em>n(L) </em>= 112
The number of students that also use a tablet, <em>T ∩ L</em> = 49
The number of students that do not use a laptop or a tablet, = 97
Required:
To organize the result of the survey in a two-way table
Solution:
U = + n(T ∪ L)
Therefore;
n(T ∪ L) = U -
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 <em>[n(L) - n(T ∩ L)] </em>= 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
The results are organized in the attached two way table and the marginal frequencies are the <u>numbers underlined</u> in the totals column
Learn more about marginal frequencies here: