The accompanying data are 45 commute times to work in minutes for workers of age 16 or older in Chicago. Construct a frequency distribution. Use a class width of 15 minutes and begin with a lower class limit of 0 minutes. Do the data amounts appear to have a normal​ distribution? Examine the data and identify anything appearing to be unique.

Construct the frequency distribution.
Commute Time​ (minutes)
Frequency
0dash  

​(Type whole​ numbers.)
Commute Times
60
15
35
30
15
45
10
15
15
 
30
12
30
30
45
20
15
45
60
15
28
30
30
60
30
45
30
12
45
20
10
15
45
45
35
20
20

Let's break down the problem and construct a frequency distribution with the given data. The steps will involve creating class intervals, tallying the frequencies, and analyzing the results.

### Given Data
Commute times (in minutes):  
```
60, 15, 35, 30, 15, 45, 10, 15, 15, 30, 12, 30, 30, 45, 20, 15, 45, 60, 15, 28, 30, 30, 60, 30, 45, 30, 12, 45, 20, 10, 15, 45, 45, 35, 20, 20.
```

### 1. Determine the class intervals
- **Class width**: 15 minutes.
- **Starting lower class limit**: 0 minutes.

The class intervals will be:
- 0–14 minutes
- 15–29 minutes
- 30–44 minutes
- 45–59 minutes
- 60–74 minutes

### 2. Tally the data into the class intervals

| Class Interval (minutes) | Frequency |
|--------------------------|-----------|
| 0–14                     | 5         |
| 15–29                    | 14        |
| 30–44                    | 13        |
| 45–59                    | 9         |
| 60–74                    | 4         |

### 3. Analyze the Data Distribution

- **Normal distribution?** The distribution is not symmetric. It is **right-skewed** because there are more values on the lower side, particularly in the first few intervals. Therefore, the data does **not appear to be normally distributed**.
  
### 4. Unique aspects of the data
- The **majority of commute times** fall within the first three intervals (0–44 minutes), indicating that most people have shorter commutes.
- Commute times of **60 minutes or more** are much less frequent, with only 4 people reporting a commute in the range of 60–74 minutes.

Would you like to ask anything more specific, such as visualizing the distribution or calculating related measures?

### Related Questions:
1. What is the mode of this dataset?
2. How does the skewness affect interpretation?
3. Can you plot a histogram for this data?
4. What are the median and mean commute times?
5. How can you calculate the variance or standard deviation for this dataset?

**Tip**: A right-skewed distribution like this one often indicates that most people have shorter commutes, while a few have significantly longer travel times.

Learn how to construct a frequency distribution for commute times in Chicago using data collected from workers. Analyze the distribution and determine if it follows a normal pattern. Suitable for students and learners interested in statistics and data analysis.

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