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. (a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result. The z-score corresponding to the individual is and indicates that the data value is standard deviation(s) V the (Type integers or decimals rounded to two decimal places as needed.) (b) Determine the quartiles. MPG Data Q, = Q2 = mpg mpg Q = mpg 32.2 35.9 42.5 O 38.7 38.9 40.2 40.6 41.3 37.8 34.3 36.4 38.1 43.0 Click to select your answer(s). 34.7 37.4 38.2 39.2 43.3 35.8 37.6 38.6 39.5 41.6 48.9
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. (a) Compute the z-score corresponding to the individual who obtained 35.8 miles per gallon. Interpret this result. The z-score corresponding to the individual is and indicates that the data value is standard deviation(s) V the (Type integers or decimals rounded to two decimal places as needed.) (b) Determine the quartiles. MPG Data Q, = Q2 = mpg mpg Q = mpg 32.2 35.9 42.5 O 38.7 38.9 40.2 40.6 41.3 37.8 34.3 36.4 38.1 43.0 Click to select your answer(s). 34.7 37.4 38.2 39.2 43.3 35.8 37.6 38.6 39.5 41.6 48.9
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![### Understanding Z-scores, Quartiles, and Outliers in MPG Data
The following data set represents the miles per gallon (MPG) of a random sample of cars with a three-cylinder, 1.0-liter engine:
#### Questions:
(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?
#### Provided Data:
Click the icon to view the data.
**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 |
#### (a) Compute the Z-score for 35.8 MPG:
The z-score corresponding to the individual who obtained 35.8 miles per gallon can be calculated using the formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( X \) = The value from the data set (35.8 MPG)
- \( \mu \) = The mean of the data set
- \( \sigma \) = The standard deviation of the data set
The z-score indicates how many standard deviations the data value is from the mean.
Please enter the values in the respective fields to compute the z-score:
\[ z = \boxed{\text{value}} \]
and indicates that the data value is \(\boxed{\text{value}}\) standard deviation(s) \(\boxed{\text{above/below}}\) the mean.
#### (b) Determine the Quartiles:
The quartiles can be found by ordering the data and determining the values at the 25th percentile (\( Q_1 \)), 50th percentile (\( Q_2 \)), and 75th percentile](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5727af85-8d91-4744-9d84-c3b258c42525%2Fd97f4edb-a538-44f5-bef1-6e633cb18922%2Fphng7e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Z-scores, Quartiles, and Outliers in MPG Data
The following data set represents the miles per gallon (MPG) of a random sample of cars with a three-cylinder, 1.0-liter engine:
#### Questions:
(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?
#### Provided Data:
Click the icon to view the data.
**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 |
#### (a) Compute the Z-score for 35.8 MPG:
The z-score corresponding to the individual who obtained 35.8 miles per gallon can be calculated using the formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( X \) = The value from the data set (35.8 MPG)
- \( \mu \) = The mean of the data set
- \( \sigma \) = The standard deviation of the data set
The z-score indicates how many standard deviations the data value is from the mean.
Please enter the values in the respective fields to compute the z-score:
\[ z = \boxed{\text{value}} \]
and indicates that the data value is \(\boxed{\text{value}}\) standard deviation(s) \(\boxed{\text{above/below}}\) the mean.
#### (b) Determine the Quartiles:
The quartiles can be found by ordering the data and determining the values at the 25th percentile (\( Q_1 \)), 50th percentile (\( Q_2 \)), and 75th percentile
Transcribed Image Text:### Statistical Analysis of Miles Per Gallon (MPG) for 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. The following statistical tasks are to be performed on this data set:
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?**
### Interquartile Range (IQR) Calculation
- To compute and interpret the interquartile range (IQR):
> The interquartile range is __ mpg. It is the range of __. (Provide values and explanation here)
### Identifying Outliers using Lower and Upper Fences
- Determine the lower and upper fences. State if there are any outliers:
> The lower fence is __.
> The upper fence is __. (Provide values and explanation here)
### Data Table Overview:
Below is the MPG data from the sample provided:
| 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 |
The data table provides the observed miles per gallon (MPG) for various cars within the specified engine category.
### Instructions
- Complete tasks by using provided data and statistical methods.
- Review the table for an accurate analysis.
- Answer all parts by filling in the blanks and related interpretations.
Click to select your answer(s).
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