1. **State the problem:** We need to construct a frequency distribution and a frequency histogram for the given reaction times data set using 8 classes. 2. **Identify the data range:** The data set is: 429, 295, 382, 337, 514, 423, 385, 430, 372, 310, 442, 387, 351, 472, 385, 413, 443, 425, 304, 453, 310, 308, 324, 412, 450, 388, 318, 357, 507, 416. - Minimum value $= 295$ - Maximum value $= 514$ 3. **Calculate class width:** Formula for class width: $$\text{Class width} = \frac{\text{Max} - \text{Min}}{\text{Number of classes}} = \frac{514 - 295}{8} = \frac{219}{8} = 27.375$$ We round up to the next whole number for class width: $28$ 4. **Determine class limits:** Start with the minimum value as the lower limit of the first class: $295$ Classes: 1. $295 - 322$ 2. $323 - 350$ 3. $351 - 378$ 4. $379 - 406$ 5. $407 - 434$ 6. $435 - 462$ 7. $463 - 490$ 8. $491 - 518$ 5. **Tally frequencies:** Count how many data points fall into each class: - Class 1 ($295-322$): 295, 310, 310, 304, 308, 318 = 6 - Class 2 ($323-350$): 337, 324, 351 (351 is in next class, so exclude) = 2 - Class 3 ($351-378$): 351, 357, 372, 382, 385, 385, 388, 387 = 8 - Class 4 ($379-406$): 382 (already counted), 385 (counted), 387 (counted), 388 (counted), 412 (next class), 413 (next class) so only 0 here - Class 5 ($407-434$): 412, 413, 416, 423, 425, 429, 430 = 7 - Class 6 ($435-462$): 442, 443, 442, 450, 453 = 5 - Class 7 ($463-490$): 472 = 1 - Class 8 ($491-518$): 507, 514 = 2 6. **Frequency distribution table:** | Class | Frequency | |-------------|-----------| | 295 - 322 | 6 | | 323 - 350 | 2 | | 351 - 378 | 8 | | 379 - 406 | 0 | | 407 - 434 | 7 | | 435 - 462 | 5 | | 463 - 490 | 1 | | 491 - 518 | 2 | 7. **Describe patterns:** The distribution shows a peak in the 351-378 class, indicating many reaction times fall in this range. There is a dip in the 379-406 class with zero frequency, suggesting no reaction times in that interval. The data is somewhat skewed with more values in the lower to middle classes. 8. **Frequency histogram:** The histogram would have bars with heights corresponding to the frequencies above, showing the distribution shape.