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Sagot :
Two way table is description of two dimensions' data and their intersections' data. The correct two-way table for the given data is:
How to form two-way table?
Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ..., Y_k[/tex]. List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
For the given case, let we suppose:
X = Ownership for skateboards
- [tex]X_1[/tex] = Student owns a skateboard
- [tex]X_2[/tex] = Student not owning skateboard
Y = Ownership for snowboards
- [tex]Y_1[/tex] = Student owns a skateboard
- [tex]Y_2[/tex] = Student not owning skateboard
Their frequencies are given in the problem as:
35 of the 99 students who own a skateboard have snowboarded.
That means [tex]n(X_1 \cap Y_1) = 33[/tex], and [tex]n(X_1)[/tex] = 99 (total frequency(number of students) is 99)
There were 13 students who have snowboarded but do not own a skateboard, so [tex]n(X_2 \cap Y_1) = 13[/tex]
147 students who have never gone snowboarding and do not own a skateboard. Thus, [tex]n(X_2 \cap Y_2) = 147[/tex]
We get the table as:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&35&n(X_1\cap Y_2)&99\\X_2&13&147&n(X_2)=13 + 147=160\\\rm Total & n(Y_1)=35+13=48 & n(Y_2) & S=160+99=259 \end{array}[/tex]
Thus, we get number of students who doesn't own snowboard but own skateboard = 99 - 35 = 64
and total students not owning either snowboard or skateboard = 35 + 147 = 182
Thus, the completed table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&35&64&99\\X_2&13&147&160\\\rm Total & 48 & 211 & 259 \end{array}[/tex]
Learn more about two way frequency table here:
https://brainly.com/question/10563783
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