The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine. (a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and upper fences. Are there any outliers? E Click the icon to view the data. MPG Data The upper fence is (Type integers or decimals. Do not round.) Are there any outliers? Select the correct choice below and, if necessary, fill, in the answer box to complete your choice. 40.2 40.6 41.3 41.6 35.9 37.8 38.1 38.2 38.6 38.7 38.9 42.5 32.2 34.3 36.4 43.0 37.4 37.6 34.7 39.2 43.3 O A. The outlier(s) is/are 35.8 39.5 48.9 (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) O B. There are no outliers. Print Done
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine. (a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and upper fences. Are there any outliers? E Click the icon to view the data. MPG Data The upper fence is (Type integers or decimals. Do not round.) Are there any outliers? Select the correct choice below and, if necessary, fill, in the answer box to complete your choice. 40.2 40.6 41.3 41.6 35.9 37.8 38.1 38.2 38.6 38.7 38.9 42.5 32.2 34.3 36.4 43.0 37.4 37.6 34.7 39.2 43.3 O A. The outlier(s) is/are 35.8 39.5 48.9 (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) O B. There are no outliers. Print Done
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Transcribed Image Text:### Statistics of Miles Per Gallon for Three-Cylinder, 1.0 Liter Engine Cars
The following tasks involve analyzing a dataset representing the miles per gallon (MPG) for a random sample of cars with a three-cylinder, 1.0 liter engine:
**(a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result.**
**(b) Determine the quartiles.**
**(c) Compute and interpret the interquartile range (IQR).**
**(d) Determine the lower and upper fences. Are there any outliers?**
**Instructions for part (c):**
Compute and interpret the interquartile range, IQR. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
The interquartile range is _______ mpg. It is the range of _______.
**Instructions for part (d):**
Determine the lower and upper fences. Are there any outliers?
The lower fence is _______.
The upper fence is _______.
(Type integers or decimals. Do not round.)
### MPG Data Table
The given MPG data is as follows:
| 32.2 | 35.9 | 37.8 | 38.7 | 38.7 | 40.2 | 42.5 |
|------|------|------|------|------|------|------|
| 34.3 | 36.4 | 38.1 | 38.9 | 40.6 | 43.0 | |
| 34.7 | 37.4 | 38.2 | 39.2 | 41.3 | 43.3 | |
| 35.8 | 37.6 | 38.6 | 39.5 | 41.6 | 48.9 | |
Use this MPG data to complete parts (c) and (d) as directed.
Click to select your answer(s).
![### Analyzing the Miles Per Gallon (MPG) Data of Three-Cylinder, 1.0 Liter Engine Cars
The accompanying data represent the miles per gallon (MPG) of a random sample of cars with a three-cylinder, 1.0-liter engine.
#### Task Breakdown:
1. **Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result.**
2. **Determine the quartiles.**
3. **Compute and interpret the interquartile range (IQR).**
4. **Determine the lower and upper fences. Are there any outliers?**
### Data
The provided MPG data points are as follows:
| MPG Data |
|----------------|
| 32.2 | 35.9 | 37.8 | 38.7 | 40.2 | 42.5 |
| 34.3 | 36.4 | 38.1 | 38.9 | 40.6 | 43.0 |
| 34.7 | 37.4 | 38.2 | 39.2 | 41.3 | 43.3 |
| 35.8 | 37.6 | 38.6 | 39.5 | 41.6 | 48.9 |
### Steps for Solving
#### (a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result.
- To find the z-score, use the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where \(X\) is the value of interest (35.8 MPG), \(\mu\) is the mean of the dataset, and \(\sigma\) is the standard deviation of the dataset.
#### (b) Determine the quartiles.
- The quartiles include:
- Q1 (First Quartile): Middle value of the first half of the data
- Q2 (Second Quartile / Median): Middle value of the data
- Q3 (Third Quartile): Middle value of the second half of the data
#### (c) Compute and interpret the interquartile range (IQR).
- IQR is calculated as:
\[
IQR = Q3 - Q1
\]
The IQR measures the spread of the middle 50](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5727af85-8d91-4744-9d84-c3b258c42525%2F95019bb9-f8e9-4c3b-9392-8a3a98328fd3%2F5qa7m6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing the Miles Per Gallon (MPG) Data of Three-Cylinder, 1.0 Liter Engine Cars
The accompanying data represent the miles per gallon (MPG) of a random sample of cars with a three-cylinder, 1.0-liter engine.
#### Task Breakdown:
1. **Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result.**
2. **Determine the quartiles.**
3. **Compute and interpret the interquartile range (IQR).**
4. **Determine the lower and upper fences. Are there any outliers?**
### Data
The provided MPG data points are as follows:
| MPG Data |
|----------------|
| 32.2 | 35.9 | 37.8 | 38.7 | 40.2 | 42.5 |
| 34.3 | 36.4 | 38.1 | 38.9 | 40.6 | 43.0 |
| 34.7 | 37.4 | 38.2 | 39.2 | 41.3 | 43.3 |
| 35.8 | 37.6 | 38.6 | 39.5 | 41.6 | 48.9 |
### Steps for Solving
#### (a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result.
- To find the z-score, use the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where \(X\) is the value of interest (35.8 MPG), \(\mu\) is the mean of the dataset, and \(\sigma\) is the standard deviation of the dataset.
#### (b) Determine the quartiles.
- The quartiles include:
- Q1 (First Quartile): Middle value of the first half of the data
- Q2 (Second Quartile / Median): Middle value of the data
- Q3 (Third Quartile): Middle value of the second half of the data
#### (c) Compute and interpret the interquartile range (IQR).
- IQR is calculated as:
\[
IQR = Q3 - Q1
\]
The IQR measures the spread of the middle 50
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