The numbers of courses taught per semester by a random sample of university professors are shown in the histogram. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. O Series1 30 25 20 15 24 10 20 16 3 1 2 4 (a) Make a frequency distribution for the data. Frequency Distribution Table f 1 2 3 4 The sample mean is, x = (Round to one decimal place as needed.) The sample standard deviation is, s = (Round to one decimal place as needed.)

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**Frequency Distribution for Course Data**

The numbers of courses taught per semester by a random sample of university professors are illustrated in the histogram below. We aim to create a frequency distribution table based on this data and use it to estimate the sample mean and sample standard deviation.

**Histogram Explanation**

- **X-axis**: Represents the number of courses taught (ranging from 1 to 4).
- **Y-axis**: Shows the frequency of professors who teach those numbers of courses.
- **Bars**:
  - 1 course: Frequency is 3
  - 2 courses: Frequency is 20
  - 3 courses: Frequency is 24
  - 4 courses: Frequency is 16

**(a) Frequency Distribution Table**

| x | f  |
|---|----|
| 1 | 3  |
| 2 | 20 |
| 3 | 24 |
| 4 | 16 |

**Calculations**

- **Sample Mean (\(\bar{x}\))**: Calculate the average number of courses taught.
- **Sample Standard Deviation (s)**: Measure the variation or dispersion of the number of courses.

The calculations will be rounded to one decimal place as needed.
Transcribed Image Text:**Frequency Distribution for Course Data** The numbers of courses taught per semester by a random sample of university professors are illustrated in the histogram below. We aim to create a frequency distribution table based on this data and use it to estimate the sample mean and sample standard deviation. **Histogram Explanation** - **X-axis**: Represents the number of courses taught (ranging from 1 to 4). - **Y-axis**: Shows the frequency of professors who teach those numbers of courses. - **Bars**: - 1 course: Frequency is 3 - 2 courses: Frequency is 20 - 3 courses: Frequency is 24 - 4 courses: Frequency is 16 **(a) Frequency Distribution Table** | x | f | |---|----| | 1 | 3 | | 2 | 20 | | 3 | 24 | | 4 | 16 | **Calculations** - **Sample Mean (\(\bar{x}\))**: Calculate the average number of courses taught. - **Sample Standard Deviation (s)**: Measure the variation or dispersion of the number of courses. The calculations will be rounded to one decimal place as needed.
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