A statistics student surveyed a sample of 36 high school students and asked, "How many days in the past week have you consumed an alcoholic beverage?" The results of the survey are shown to the right. Use these results to answer parts (a) through (d).
A statistics student surveyed a sample of 36 high school students and asked, "How many days in the past week have you consumed an alcoholic beverage?" The results of the survey are shown to the right. Use these results to answer parts (a) through (d).
MATLAB: An Introduction with Applications
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![A statistics student surveyed a sample of 36 high school students and asked, "How many days in the past week have you consumed an alcoholic beverage?" The results of the survey are shown to the right. Use these results to answer parts (a) through (d).
The table of responses is as follows:
\[
\begin{array}{cccccc}
0 & 1 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 4 \\
1 & 5 & 1 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 & 0 & 1 \\
1 & 1 & 0 & 1 & 0 & 0 \\
0 & 1 & 1 & 2 & 3 & 2 \\
\end{array}
\]
**(a) Is this data discrete or continuous?**
- **A.** Discrete, because the data are countable
- **B.** Continuous, because the data are not countable
- **C.** Continuous, because the data are countable
- **D.** Discrete, because the data are not countable
**(b) Draw a histogram of the data and describe its shape. Choose the histogram below that correctly depicts the given data.**
- **Options:**
- **A.** Histogram showing a uniform distribution
- **B.** Histogram with a peak at lower values skewed right
- **C.** Histogram showing a bell-shaped distribution
- **D.** Histogram with a peak at lower values skewed left
**Describe the shape of the distribution. Choose the correct answer below.**
- **A.** The distribution is symmetric and bell-shaped.
- **B.** The distribution is skewed left.
### Explanation of Graphs:
- **Histogram A:** Shows a somewhat even distribution of responses across all values, suggesting a uniform distribution.
- **Histogram B:** Shows a peak at lower values with a tail extending towards higher values, indicating a right-skewed distribution.
- **Histogram C:** Shows a symmetric distribution around a central value, indicating a bell-shaped distribution.
- **Histogram D:** Shows a peak at lower values with a tail extending towards lower values, indicating a left-skewed distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F358f2374-ec0b-47e3-b3ef-a3300df189bd%2F843b6286-2a7d-4c84-b95b-b8b8b894b396%2Fzteqs5n_processed.png&w=3840&q=75)
Transcribed Image Text:A statistics student surveyed a sample of 36 high school students and asked, "How many days in the past week have you consumed an alcoholic beverage?" The results of the survey are shown to the right. Use these results to answer parts (a) through (d).
The table of responses is as follows:
\[
\begin{array}{cccccc}
0 & 1 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 4 \\
1 & 5 & 1 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 & 0 & 1 \\
1 & 1 & 0 & 1 & 0 & 0 \\
0 & 1 & 1 & 2 & 3 & 2 \\
\end{array}
\]
**(a) Is this data discrete or continuous?**
- **A.** Discrete, because the data are countable
- **B.** Continuous, because the data are not countable
- **C.** Continuous, because the data are countable
- **D.** Discrete, because the data are not countable
**(b) Draw a histogram of the data and describe its shape. Choose the histogram below that correctly depicts the given data.**
- **Options:**
- **A.** Histogram showing a uniform distribution
- **B.** Histogram with a peak at lower values skewed right
- **C.** Histogram showing a bell-shaped distribution
- **D.** Histogram with a peak at lower values skewed left
**Describe the shape of the distribution. Choose the correct answer below.**
- **A.** The distribution is symmetric and bell-shaped.
- **B.** The distribution is skewed left.
### Explanation of Graphs:
- **Histogram A:** Shows a somewhat even distribution of responses across all values, suggesting a uniform distribution.
- **Histogram B:** Shows a peak at lower values with a tail extending towards higher values, indicating a right-skewed distribution.
- **Histogram C:** Shows a symmetric distribution around a central value, indicating a bell-shaped distribution.
- **Histogram D:** Shows a peak at lower values with a tail extending towards lower values, indicating a left-skewed distribution.
Transcribed Image Text:### Survey Data Analysis on Alcohol Consumption
A statistics student surveyed a sample of 36 high school students, asking, "How many days in the past week have you consumed an alcoholic beverage?" The results of the survey are displayed in a table showing the frequency of responses for each number of days, from 0 to 5.
#### Frequency Distribution Table
| Days | Frequency |
|------|-----------|
| 0 | 11 |
| 1 | 11 |
| 2 | 5 |
| 3 | 4 |
| 4 | 3 |
| 5 | 2 |
#### Graphical Representation
The data is illustrated through four graphs, each showing the distribution of responses for different ranges of days.
- **Graph 1:** Shows a bar graph with a relatively symmetrical distribution, centered around 0 and 1.
- **Graph 2:** Another graphical representation which looks similar with slight variations in frequency.
- **Graph 3 & Graph 4:** These graphs continue to display data alignment in a histographic form, maintaining a focus on symmetry or slight skewness.
#### Describe the Shape of the Distribution
Four options are provided for describing the shape of the distribution:
- **A.** The distribution is symmetric and bell-shaped.
- **B.** The distribution is skewed left.
- **C.** The distribution is skewed right.
- **D.** The distribution is symmetric, but not bell-shaped.
#### Statistical Measures
- **(c) Compute the Mean and Median**
- **Mean:** Calculate the average number of days using the frequency table.
- **Median:** Determine the median as the middle value when the days are ordered numerically.
- **(d) Determine the Mode**
- **Mode:** Identify the number of days that appears most frequently in the data.
By analyzing these distributions and calculations, the study aims to understand high school students' alcohol consumption behaviors over a week.
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