1. **State the problem:** Find the 94th percentile (P94) from the given data set. 2. **List the data:** The data points are: 100, 190, 200, 250, 290, 300, 420, 430, 500, 530, 550, 560, 580, 610, 620, 630, 660, 670, 680, 720, 730, 790, 810, 830, 870, 890, 930, 950, 960, 980 3. **Sort the data:** The data is already sorted in ascending order. 4. **Count the number of data points:** There are $n=30$ data points. 5. **Formula for percentile position:** $$ L = \frac{P}{100} \times (n+1) $$ where $P=94$ is the percentile. 6. **Calculate the position:** $$ L = \frac{94}{100} \times (30+1) = 0.94 \times 31 = 29.14 $$ 7. **Interpret the position:** The 94th percentile lies between the 29th and 30th data points. 8. **Identify the 29th and 30th data points:** - 29th data point = 960 - 30th data point = 980 9. **Interpolate to find P94:** $$ P94 = x_{29} + (L - 29) \times (x_{30} - x_{29}) $$ $$ P94 = 960 + (29.14 - 29) \times (980 - 960) = 960 + 0.14 \times 20 = 960 + 2.8 = 962.8 $$ 10. **Final answer:** The 94th percentile $P94$ is approximately **962.8**.