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 stimulus430
386
350
300
450
291
426
469
451
386
382
373
386
309
322
333
310
414
307
361
514
444
441
325
510
421
389
426
410
415

To construct a frequency distribution and a frequency histogram for the given data set with 8 classes, we need to follow these steps:

1. **Determine the range of the dataTo construct a frequency distribution and a frequency histogram for the given data set with 8 classes, we need to follow these steps:

1. **Determine the range of the **
   - The smallest value (minimum) in the data set is 291.
   - The largest value (maximum) in the data set is 514.
   - Range = Maximum - Minimum = 514 - 291 = 223

2. **Determine the class width:**
   - Class width = Range / Number of classes
   - Class width ≈ 223 / 8 ≈ 27.875
   - We can round up the class width to 28 for simplicity.

3. **Determine the class limits:**
   - The first class lower limit is 291 (the minimum value).
   - Each subsequent class lower limit is the previous lower limit plus the class width.
   - This process continues until we have 8 classes.

4. **Construct the frequency distribution table:**

| Class Limits | Frequency |
|--------------|-----------|
| 291 - 318    | 4         |
| 319 - 346    | 3         |
| 347 - 374    | 4         |
| 375 - 402    | 6         |
| 403 - 430    | 6         |
| 431 - 458    | 3         |
| 459 - 486    | 2         |
| 487 - 514    | 2         |

5. **Construct the frequency histogram:**

To visualize the data, plot the frequency histogram using the class limits on the x-axis and the frequencies on the y-axis.

Let's create the frequency distribution and histogram using Python for accuracy:

```python
import pandas as pd
import matplotlib.pyplot as plt

# Data set
data = [430, 386, 350, 300, 450, 291, 426, 469, 451, 386, 382, 373, 386, 309, 322, 333, 310, 414, 307, 361, 514, 444, 441, 325, 510, 421, 389, 426, 410, 415]

# Define the number of classes and class width
num_classes = 8
class_width = 28

# Determine the class limits
min_value = min(data)
max_value = max(data)

# Create bins for the histogram
bins = [min_value + i * class_width for i in range(num_classes + 1)]

# Create the frequency distribution table
frequency_distribution = pd.cut(data, bins=bins, right=False).value_counts().sort_index()

# Plot the frequency histogram
plt.figure(figsize=(10, 6))
plt.hist(data, bins=bins, edgecolor='black')
plt.title('Frequency Histogram of Reaction Times')
plt.xlabel('Reaction Time (milliseconds)')
plt.ylabel('Frequency')
plt.xticks(bins)
plt.grid(axis='y')
plt.show()

frequency_distribution
```

Running the above code will provide the frequency distribution and display the histogram.

**Patterns observed:**
- The data appears to be somewhat symmetrically distributed, with the most frequent reaction times falling between 375 and 430 milliseconds.
- There are no outliers in the data set.
- The distribution shows a peak in the middle classes, suggesting that most reaction times are around the center of the range.

Would you like more details or have any questions?

Here are 5 numbered questions you might want to ask:

1. How do you calculate the class boundaries for a frequency distribution?
2. What are the differences between a histogram and a bar chart?
3. How can you determine the number of classes to use in a frequency distribution?
4. What other types of graphs can be used to represent this data set?
5. How can skewness in data be detected from a frequency histogram?

**Tip:** Always ensure the class width is chosen such that it covers the entire range of data without leaving gaps or overlaps between the classes.

Learn how to construct a frequency distribution and a frequency histogram for reaction times data using 8 classes. Understand the patterns in the distribution of reaction times of 30 adult females to an auditory stimulus.

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