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

 429  293  382  335  514  421  389  430  375  313  444  388  350  470  389  413  441  429  303  455  310  310  324  410  450  389  321  357  506  417


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

### Step 1: Calculate the Range
First, we need to find the range of the data set.
- **Maximum value** = 514 ms
- **Minimum value** = 293 ms
- **Range** = \( 514 - 293 = 221 \) ms

### Step 2: Determine the Class Width
To determine the class width, we use the formula:
\[
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} \approx \frac{221}{8} \approx 27.625
\]
We round this up to the nearest whole number, which is 28.

### Step 3: Create the Class Intervals
Now, we define the class intervals by starting with the minimum value and adding the class width:

1. **Class 1:** 293 - 320
2. **Class 2:** 321 - 348
3. **Class 3:** 349 - 376
4. **Class 4:** 377 - 404
5. **Class 5:** 405 - 432
6. **Class 6:** 433 - 460
7. **Class 7:** 461 - 488
8. **Class 8:** 489 - 516

### Step 4: Tally the Frequencies
Now, we'll count how many data points fall into each class interval:

1. **293 - 320**: 5
2. **321 - 348**: 4
3. **349 - 376**: 4
4. **377 - 404**: 9
5. **405 - 432**: 5
6. **433 - 460**: 2
7. **461 - 488**: 0
8. **489 - 516**: 1

### Step 5: Construct the Frequency Distribution Table

| Class Interval | Frequency |
|----------------|-----------|
| 293 - 320      | 5         |
| 321 - 348      | 4         |
| 349 - 376      | 4         |
| 377 - 404      | 9         |
| 405 - 432      | 5         |
| 433 - 460      | 2         |
| 461 - 488      | 0         |
| 489 - 516      | 1         |

### Step 6: Draw the Frequency Histogram
- **X-axis**: Class intervals
- **Y-axis**: Frequencies
- Each bar height corresponds to the frequency of each class interval.

### Step 7: Describe the Patterns
Looking at the frequency distribution and histogram:
- The reaction times are concentrated mostly in the middle intervals, with the highest frequency in the 377 - 404 ms range.
- The data appears to be somewhat right-skewed since the tail extends more towards the higher values.
- There is a clear decrease in frequency as we move to higher reaction times, indicating that fewer individuals had longer reaction times.

Would you like a more detailed explanation or have any questions?

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**Relative Questions:**
1. How would the frequency distribution change if we increased the number of classes to 10?
2. What does the shape of the histogram suggest about the underlying distribution of reaction times?
3. How could we use this frequency distribution to estimate the probability of a reaction time falling within a specific interval?
4. What is the significance of the skewness observed in the histogram?
5. How would changing the class width affect the appearance of the histogram?

**Tip:** When choosing the number of classes, try different class widths to see how it affects the representation of the data.

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: 429 293 382 335 514 421 389 430 375 313 444 388 350 470 389 413 441 429 303 455 310 310 324 410 450 389 321 357 506 417

Learn how to construct a frequency distribution and histogram for the reaction times of 30 adult females with a detailed step-by-step solution. This problem involves calculating the range, determining class width, and analyzing the patterns in the data. Suitable for students in Grades 10-12.

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