To determine the largest discrepancy between the experimental and expected probabilities in Jade's experiment, we first need to compute both the experimental probabilities from the given frequencies and the expected probabilities if each outcome were equally likely.
Step 1: Total Frequency
First, we calculate the total number of tosses:
\[ \text{Total Frequency} = 10 + 9 + 6 + 15 + 13 + 8 = 61 \]
Step 2: Experimental Probabilities
Next, we find the experimental probabilities for each outcome by dividing the frequency of each outcome by the total frequency:
\[ \text{P(2)} = \frac{10}{61} \approx 0.1639 \]
\[ \text{P(4)} = \frac{9}{61} \approx 0.1475 \]
\[ \text{P(6)} = \frac{6}{61} \approx 0.0984 \]
\[ \text{P(8)} = \frac{15}{61} \approx 0.2459 \]
\[ \text{P(10)} = \frac{13}{61} \approx 0.2131 \]
\[ \text{P(12)} = \frac{8}{61} \approx 0.1311 \]
Step 3: Expected Probabilities
Assuming each outcome (2, 4, 6, 8, 10, 12) is equally likely, the expected probability for each would be:
\[ \text{Expected Probability} = \frac{1}{6} \approx 0.1667 \]
Step 4: Discrepancies
Now, we calculate the discrepancies for each outcome by taking the absolute difference between the experimental and expected probabilities:
\[ \text{Discrepancy for 2} = |0.1639 - 0.1667| \approx 0.0028 \]
\[ \text{Discrepancy for 4} = |0.1475 - 0.1667| \approx 0.0192 \]
\[ \text{Discrepancy for 6} = |0.0984 - 0.1667| \approx 0.0683 \]
\[ \text{Discrepancy for 8} = |0.2459 - 0.1667| \approx 0.0792 \]
\[ \text{Discrepancy for 10} = |0.2131 - 0.1667| \approx 0.0464 \]
\[ \text{Discrepancy for 12} = |0.1311 - 0.1667| \approx 0.0356 \]
Step 5: Largest Discrepancy
After calculating all the discrepancies, we find the largest discrepancy:
- For outcome 8: 0.0792 is the highest.
Thus, the outcome value with the largest discrepancy between the experimental and expected probability is 8, with a discrepancy of approximately 0.0792.