The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint for "30+ hours." 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. wClick the icon to view the pie chart. First construct the frequency distribution. Class Frequency, f 0-4 5-9 10-14 15-19 20-24 25-29 30+ Find an approximation for the sample mean. x= (Type an integer or decimal rounded to the nearest tenth as needed.) Find an approximation for the sample standard deviation. s= (Type an integer or decimal rounded to the nearest tenth as needed.)

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### Distribution of Hours Spent Doing Chores

The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint for "30+ hours." 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.

[Insert link to view the pie chart]

#### Frequency Distribution Table

| Class | Frequency, f |
|-------|--------------|
| 0-4   |              |
| 5-9   |              |
| 10-14 |              |
| 15-19 |              |
| 20-24 |              |
| 25-29 |              |
| 30+   |              |

#### Estimation of Statistical Measures

1. **Sample Mean (x̄):**

   \[
   \bar{x} = \text{ [Type an integer or decimal rounded to the nearest tenth as needed.]}
   \]

2. **Sample Standard Deviation (s):**

   \[
   s = \text{ [Type an integer or decimal rounded to the nearest tenth as needed.]}
   \]

### Instructions for Calculations

1. **Constructing the Frequency Distribution:**
   - Begin by filling in the frequency (f) for each class interval based on the data provided in the pie chart.

2. **Estimation of Sample Mean (x̄):**
   - Calculate the midpoint for each class interval.
   - Multiply the midpoint by the frequency for each class, and then sum these products.
   - Divide the sum by the total number of frequencies to get the sample mean.

3. **Estimation of Sample Standard Deviation (s):**
   - Calculate the squared difference between each midpoint and the sample mean.
   - Multiply these squared differences by the frequencies of each class.
   - Sum these values and divide by the total number of frequencies minus one.
   - Take the square root of the result to obtain the sample standard deviation. 

This exercise demonstrates how to analyze a distribution using a frequency distribution table and compute essential statistical measures. The pie chart visualization assists in understanding the distribution of time spent on chores by different individuals within a sample.
Transcribed Image Text:### Distribution of Hours Spent Doing Chores The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint for "30+ hours." 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. [Insert link to view the pie chart] #### Frequency Distribution Table | Class | Frequency, f | |-------|--------------| | 0-4 | | | 5-9 | | | 10-14 | | | 15-19 | | | 20-24 | | | 25-29 | | | 30+ | | #### Estimation of Statistical Measures 1. **Sample Mean (x̄):** \[ \bar{x} = \text{ [Type an integer or decimal rounded to the nearest tenth as needed.]} \] 2. **Sample Standard Deviation (s):** \[ s = \text{ [Type an integer or decimal rounded to the nearest tenth as needed.]} \] ### Instructions for Calculations 1. **Constructing the Frequency Distribution:** - Begin by filling in the frequency (f) for each class interval based on the data provided in the pie chart. 2. **Estimation of Sample Mean (x̄):** - Calculate the midpoint for each class interval. - Multiply the midpoint by the frequency for each class, and then sum these products. - Divide the sum by the total number of frequencies to get the sample mean. 3. **Estimation of Sample Standard Deviation (s):** - Calculate the squared difference between each midpoint and the sample mean. - Multiply these squared differences by the frequencies of each class. - Sum these values and divide by the total number of frequencies minus one. - Take the square root of the result to obtain the sample standard deviation. This exercise demonstrates how to analyze a distribution using a frequency distribution table and compute essential statistical measures. The pie chart visualization assists in understanding the distribution of time spent on chores by different individuals within a sample.
### Weekly Study Hours Analysis

The weekly study hours of students have been analyzed and presented in a pie chart. The pie chart visually represents the distribution of study hours among different groups of students. The chart is divided into sections, each corresponding to a range of study hours and the number of students within that range. Below is a detailed description of the chart:

#### Pie Chart Key
- **0-4 hours**: Represented in blue (6 people)
- **5-9 hours**: Represented in red (10 people)
- **10-14 hours**: Represented in yellow-green (25 people)
- **15-19 hours**: Represented in light green (19 people)
- **20-24 hours**: Represented in turquoise (15 people)
- **25-29 hours**: Represented in purple (9 people)
- **30+ hours**: Represented in pink (4 people)

#### Analysis
- **Most Common Study Range**: The majority of students (25) fall in the 10-14 hours range.
- **Least Common Study Range**: Only 4 students study for more than 30 hours a week.
- **Varied Study Habits**: The data shows a wide distribution of study habits, indicating a mix of study intensities among students.

### Conclusion
This analysis provides an insightful look into the study patterns of students, which can be pivotal for academic planning and resource allocation.

### [Print](#) | [Done](#)

---

This data supports educational institutions in understanding student study patterns, which is crucial for optimizing academic support services.
Transcribed Image Text:### Weekly Study Hours Analysis The weekly study hours of students have been analyzed and presented in a pie chart. The pie chart visually represents the distribution of study hours among different groups of students. The chart is divided into sections, each corresponding to a range of study hours and the number of students within that range. Below is a detailed description of the chart: #### Pie Chart Key - **0-4 hours**: Represented in blue (6 people) - **5-9 hours**: Represented in red (10 people) - **10-14 hours**: Represented in yellow-green (25 people) - **15-19 hours**: Represented in light green (19 people) - **20-24 hours**: Represented in turquoise (15 people) - **25-29 hours**: Represented in purple (9 people) - **30+ hours**: Represented in pink (4 people) #### Analysis - **Most Common Study Range**: The majority of students (25) fall in the 10-14 hours range. - **Least Common Study Range**: Only 4 students study for more than 30 hours a week. - **Varied Study Habits**: The data shows a wide distribution of study habits, indicating a mix of study intensities among students. ### Conclusion This analysis provides an insightful look into the study patterns of students, which can be pivotal for academic planning and resource allocation. ### [Print](#) | [Done](#) --- This data supports educational institutions in understanding student study patterns, which is crucial for optimizing academic support services.
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