Question

2 tables. A 4-column table with 3 rows is titled Frequency Two-way table. Column 1 has entries boys, girls, total. Column 2 is labeled 4-year with entries 76, 83, 159. Column 3 is labeled 2-year with entries 34, 38, 72. Column 4 is labeled total with entries 110, 121, 231.A 4-column table with 2 rows titled Relative frequency table by rows. Column 1 has entries boys, girls. Column 2 is labeled 4-year with entries a, c. Column 3 is labeled 2-year with entries b, d. Column 4 is labeled Total with entries 100 percent, 100 percent.
Determine the values to complete the Relative Frequency by Rows table.

a =

b =
c =
d =

Answer 1

To find the values for the relative frequency table by rows, we need to calculate the relative frequencies for each category based on the counts from the Frequency Two-way table.

Given the data in the Frequency Two-way table:

| | 4-year | 2-year | Total |
|---------|--------|--------|-------|
| Boys | 76 | 34 | 110 |
| Girls | 83 | 38 | 121 |
| Total | 159 | 72 | 231 |

The relative frequency for each category is calculated by dividing the frequency of that category by the total for that row.

### For Boys:
1. **4-year (a)**:
\[
a = \frac{76}{110} \approx 0.6909 \text{ (or 69.09\% when expressed as a percentage)}
\]

2. **2-year (b)**:
\[
b = \frac{34}{110} \approx 0.3091 \text{ (or 30.91\% when expressed as a percentage)}
\]

### For Girls:
1. **4-year (c)**:
\[
c = \frac{83}{121} \approx 0.6860 \text{ (or 68.60\% when expressed as a percentage)}
\]

2. **2-year (d)**:
\[
d = \frac{38}{121} \approx 0.3140 \text{ (or 31.40\% when expressed as a percentage)}
\]

Putting these values into the Relative Frequency by Rows table:

\[
\begin{align*}
a & \approx 0.6909 \text{ (or 69.09\%)} \\
b & \approx 0.3091 \text{ (or 30.91\%)} \\
c & \approx 0.6860 \text{ (or 68.60\%)} \\
d & \approx 0.3140 \text{ (or 31.40\%)}
\end{align*}
\]

Thus, the values for the Relative Frequency by Rows table are approximately:
- **a = 0.6909**
- **b = 0.3091**
- **c = 0.6860**
- **d = 0.3140**