Questions: Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns. Number of classes: 8 Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus 426, 295, 383, 336, 514, 425, 389, 430, 374, 313, 443, 386, 350, 467, 389, 412, 444, 429, 305, 451, 307, 307, 325, 413, 450, 389, 320, 358, 510, 418 Construct a frequency distribution of the data. Use the minimum data entry as the lower limit of the first class. Class 1. 295-322 Frequency 2. 323-350 3 3. 351-378 2 4. 379-406 5. 407-434 6. 435-462 4 7. 463-490 8. 491-518

Solution Steps

To construct a frequency distribution and histogram, follow these steps:

1. Determine the range of each class based on the given class intervals.
2. Count the number of data points that fall into each class to find the frequency.
3. Use the frequencies to create a histogram.

To construct a frequency distribution, we first need to determine the class width. The formula for class width is:

\[ \text{Class Width} = \frac{\text{Maximum Value} - \text{Minimum Value}}{\text{Number of Classes}} \]

From the data set, the maximum value is 514 and the minimum value is 295. The number of classes is 8.

\[ \text{Class Width} = \frac{514 - 295}{8} = \frac{219}{8} = 27.375 \]

We round up to the nearest whole number, so the class width is 28.

Starting with the minimum value of 295, we construct the class intervals:

1. \(295 - 322\)
2. \(323 - 350\)
3. \(351 - 378\)
4. \(379 - 406\)
5. \(407 - 434\)
6. \(435 - 462\)
7. \(463 - 490\)
8. \(491 - 518\)

Count the number of data points in each class interval:

1. \(295 - 322\): 5
2. \(323 - 350\): 3
3. \(351 - 378\): 2
4. \(379 - 406\): 5
5. \(407 - 434\): 6
6. \(435 - 462\): 4
7. \(463 - 490\): 2
8. \(491 - 518\): 3

Final Answer