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:
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4-year (a): \[ a = \frac{76}{110} \approx 0.6909 \text{ (or 69.09% when expressed as a percentage)} \]
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2-year (b): \[ b = \frac{34}{110} \approx 0.3091 \text{ (or 30.91% when expressed as a percentage)} \]
For Girls:
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4-year (c): \[ c = \frac{83}{121} \approx 0.6860 \text{ (or 68.60% when expressed as a percentage)} \]
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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