Exercise 4 Page 686

It is also possible to find conditional frequencies using only the original two-way frequency table.

	In Favor of Planting a Community Garden
Gender	Yes	No	Total
Girls	71	17	88
Boys	61	35	96
Total	132	52	184

We can divide the number of responses in each cell by the conditional total — either the column total or the row total depending on which condition is being considered. In this case, we want to know the conditional frequencies by row.

	In Favor of Planting a Community Garden
Gender	Yes	No
Girls	71/88≈ 0.807	17/88≈ 0.193
Boys	61/96≈ 0.635	35/96≈ 0.365

To see why this works, let's consider just the first cell from the original solution. 0.386/0.478≈ 0.807 Where did the values on the left-hand side of this approximation come from? Recall that they are the joint relative frequency and the marginal relative frequency. Joint relative frequency/Marginal relative frequency → 0.386/0.478 The joint relative frequencies are found by dividing the individual cell values by the grand total and the marginal relative frequencies are found by dividing the row and column totals by the grand total. For this one cell, we had the following numbers. 71/184≈ 0.368 and 88/184≈ 0.478 Let's now see what happens when we find the conditional relative frequency using the fractions rather than using the rounded decimal numbers. We end up with the same fraction that was used to calculate the conditional frequency in the alternative solution method!