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We are given a two-way frequency table with some missing joint frequencies.
The frequencies in the total row and column are called "marginal frequencies"
The frequencies in the other rows and columns are called "joint frequencies"
Let us first find the joint frequency "Single Item and Tip"
[tex]\begin{gathered} x+60=150 \\ x=150-60 \\ x=90 \end{gathered}[/tex]So, the joint frequency "Single Item and Tip" is 90 (option B)
Now, let us find the joint frequency "Single Item and No Tip"
[tex]\begin{gathered} 90+x=360 \\ x=360-90 \\ x=270 \end{gathered}[/tex]So, the joint frequency "Single Item and No Tip" is 270 (option D)
Now first we need to find the marginal frequency as below
[tex]\begin{gathered} 360+x=500 \\ x=500-360 \\ x=140 \end{gathered}[/tex]Finally, now we can find the joint frequency "Multiple Items and No Tip"
[tex]\begin{gathered} 60+x=140 \\ x=140-60 \\ x=80 \end{gathered}[/tex]So, the joint frequency "Multiple Items and No Tip" is 80 (option A)
Therefore, the missing joint frequencies are
Option A
Option B
Option D
