Question

which could be a conditional relative frequency table?

	a	b	total
d	0.25	0.25	0.50
total	0.50	0.50	1.0

	a	b	total
d	0.35	0.65	1.0
total	0.30	0.70	1.0

	a	b	total

Explanation:

To determine a conditional relative frequency table, we recall that in a conditional relative frequency table (either row - wise or column - wise), the sum of the relative frequencies in each row (or each column) should be equal to 1.0.

Analyze the first table:

• Rows: For row \(C\), the sum of the relative frequencies is \(0.25 + 0.25=0.50

eq1.0\). For row \(D\), the sum of the relative frequencies is \(0.25 + 0.25 = 0.50
eq1.0\). So this is not a conditional relative frequency table (since the row totals are not 1.0, and if we consider column - wise, the column totals are 0.50 as well, not 1.0).

Analyze the second table:

• Rows: For row \(C\), the sum of the relative frequencies is \(0.25+0.75 = 1.0\). For row \(D\), the sum of the relative frequencies is \(0.35 + 0.65=1.0\).
• Columns: For column \(A\), the sum of the relative frequencies is \(0.25+0.35 = 0.60\)? Wait, no, wait the "Total" row for column \(A\) is \(0.30\) and column \(B\) is \(0.70\). Wait, actually, in a conditional relative frequency table, if we calculate row - conditional relative frequencies, each row should sum to 1.0. In this table, row \(C\) sums to \(0.25 + 0.75=1.0\) and row \(D\) sums to \(0.35+0.65 = 1.0\). This is consistent with a row - conditional relative frequency table (where we calculate relative frequencies within each row).

Analyze the third table:

• The table is incomplete (only row \(C\) is shown, and the total for row \(C\) is \(0.50\) instead of \(1.0\) if it were a conditional relative frequency table for row \(C\)). Also, there is no row \(D\) or a total row for columns. So it is not a valid conditional relative frequency table.

So the second table (the one with rows \(C\) and \(D\) where each row sums to 1.0) is a conditional relative frequency table.

Answer:

The table with rows \(C\) (with values \(0.25\), \(0.75\), \(1.0\)) and \(D\) (with values \(0.35\), \(0.65\), \(1.0\)) and column totals \(0.30\), \(0.70\), \(1.0\) (the second table among the given options)