Question

HELP AND EXPLAIN

Answer 1

The relative frequency of 15/24 for this considered situation represents the situation given by: Option C: Out of all the family members that prefer a lake, 15 are children.

How to find the relative frequency?

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency). (subgroup being group defined by a row, or a column)

How to form two-way table?

Suppose two dimensions are there, viz X and Y. Some values of X are there as $X_1, X_2, ... , X_n$ and some values of Y are there as $Y_1, Y_2, ... , Y_n$

List them in title of the rows and left to the columns. There will be $n \times k$ table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of $X_i$ and $Y_j$ (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:

$\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}$

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.

The given two-way frequency table is:

                                        Lake                  Hike                       Total

Children                                                       6

Adults                                 9

Total                                                             14                            38

Total of hike subgroup is 14, out of which children are 6, so adults going for hiking must be 14 - 6 = 8 as adults and children going for hiking together are 14 in counts.

So, we get:
n(Hike ∩ Children) = 8

Thus, the total of subgroup Adults is 9+8=17 = n(Adults)

Total of vertical total columns is: n(Children) + n(Adults) = 38

or, we get: n(Children) = 38 - 17=  21

Since total of children subgroup is:

n(Lake ∩ Children) + n(Hike ∩ Children) = n(Children)

Thus, we get:
n(Lake ∩ Children) + 6 = 21

n(Lake ∩ Children) = 21-6 = 15

Thus, sum of the 'lake' subgroup is:

n(Lake) = n( Lake ∩ Children) + n(Lake ∩ Adults)

n(Lake) = 15 + 9 = 24

Thus, the completed two-way table is:

                                        Lake                  Hike                       Total

Children                             15                        6                             21

Adults                                 9                         8                             17

Total                                   24                       14                            38

Now, we've to find what does 15/24 represents.

The division is done by 24, which is the total of "lake" subgroup.

And in that lake subgroup, we have:

n(Lake ∩ Children) = 15

Thus, 15/24 is the relative frequency of those children who prefer the lake, relative to total number of people who prefer lake.

Thus, the relative frequency of 15/24 for this considered situation represents the situation given by: Option C: Out of all the family members that prefer a lake, 15 are children.

Learn more about conditional relative frequency here:

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