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 48.9 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? Click the icon to view the data. (a) Compute the z-score corresponding to the individual who obtained 48.9 miles per gallon. Interpret this result. standard deviation(s) The Z-score corresponding to the individual is and indicates that the data value is (Type integers or decimals rounded to two decimal places as needed.) X MPG Data 32.7 42.3 D 35.9 37.9 38.6 40.1 38.1 39.0 40.6 42.5 34.2 36.2 34.7 37.4 38.3 39.4 41.4 43.5 35.3 37.7 38.5 39.6 41.6 48.9 the
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 48.9 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? Click the icon to view the data. (a) Compute the z-score corresponding to the individual who obtained 48.9 miles per gallon. Interpret this result. standard deviation(s) The Z-score corresponding to the individual is and indicates that the data value is (Type integers or decimals rounded to two decimal places as needed.) X MPG Data 32.7 42.3 D 35.9 37.9 38.6 40.1 38.1 39.0 40.6 42.5 34.2 36.2 34.7 37.4 38.3 39.4 41.4 43.5 35.3 37.7 38.5 39.6 41.6 48.9 the
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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![### Statistical Analysis: Miles Per Gallon (MPG) Data for Cars
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0-liter engine.
#### Tasks:
(a) Compute the z-score corresponding to the individual who obtained 48.9 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?
**Data Table (MPG Data):**
| 32.7 | 35.9 | 37.9 | 38.6 | 40.1 | 42.3 |
|------|------|------|------|------|------|
| 34.2 | 36.2 | 38.1 | 39.0 | 40.6 | 42.5 |
| 34.7 | 37.4 | 38.3 | 39.4 | 41.4 | 43.5 |
| 35.3 | 37.7 | 38.5 | 39.6 | 41.6 | 48.9 |
### Steps and Calculations:
(a) **Compute the z-score corresponding to the individual who obtained 48.9 miles per gallon. Interpret this result.**
The z-score corresponding to the individual is ____ and indicates that the data value is ____ standard deviation(s) (above/below) the (mean).
**Note:** The z-score calculation formula is as follows:
\[ z = \frac{X - \mu}{\sigma} \]
where \(X\) is the data value (48.9 miles per gallon), \(\mu\) is the mean of the data set, and \(\sigma\) is the standard deviation of the data set.
(b) **Determine the quartiles.**
(c) **Compute and interpret the interquartile range (IQR).**
**Note:** The IQR is computed as:
\[ \text{IQR} = Q3 - Q1 \]
where \( Q3 \) is the third quartile and \( Q1 \) is the first quartile.
(d) **Determine the lower and upper fences. Are there any outliers?**
**Note:** The lower and upper fences can be calculated using:
\[ \text{Lower Fence} = Q1 -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbaaf3a5-97a4-44d4-82b4-c685cbb2fa1a%2F520db4aa-db9c-4c6f-9ace-a8c6f3bc3c50%2Fixsx6rd_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis: Miles Per Gallon (MPG) Data for Cars
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0-liter engine.
#### Tasks:
(a) Compute the z-score corresponding to the individual who obtained 48.9 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?
**Data Table (MPG Data):**
| 32.7 | 35.9 | 37.9 | 38.6 | 40.1 | 42.3 |
|------|------|------|------|------|------|
| 34.2 | 36.2 | 38.1 | 39.0 | 40.6 | 42.5 |
| 34.7 | 37.4 | 38.3 | 39.4 | 41.4 | 43.5 |
| 35.3 | 37.7 | 38.5 | 39.6 | 41.6 | 48.9 |
### Steps and Calculations:
(a) **Compute the z-score corresponding to the individual who obtained 48.9 miles per gallon. Interpret this result.**
The z-score corresponding to the individual is ____ and indicates that the data value is ____ standard deviation(s) (above/below) the (mean).
**Note:** The z-score calculation formula is as follows:
\[ z = \frac{X - \mu}{\sigma} \]
where \(X\) is the data value (48.9 miles per gallon), \(\mu\) is the mean of the data set, and \(\sigma\) is the standard deviation of the data set.
(b) **Determine the quartiles.**
(c) **Compute and interpret the interquartile range (IQR).**
**Note:** The IQR is computed as:
\[ \text{IQR} = Q3 - Q1 \]
where \( Q3 \) is the third quartile and \( Q1 \) is the first quartile.
(d) **Determine the lower and upper fences. Are there any outliers?**
**Note:** The lower and upper fences can be calculated using:
\[ \text{Lower Fence} = Q1 -
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