Alternative Formula You used S S x = Σ ( x − x ¯ ) 2 when calculating variance and standard deviation. An alternative formula that is sometimes more convenient for hand calculations is S S x = Σ x 2 − ( Σ x ) 2 n . You can find the sample variance by dividing the sum of squares by n − 1 and the sample standard deviation by finding the square root of the sample variance. (a) Show how to obtain the alternative formula. (b) Use the alternative formula to calculate the sample standard deviation for the data set in Exercise 15. (c) Compare your result with the sample standard deviation obtained in Exercise 15.
Alternative Formula You used S S x = Σ ( x − x ¯ ) 2 when calculating variance and standard deviation. An alternative formula that is sometimes more convenient for hand calculations is S S x = Σ x 2 − ( Σ x ) 2 n . You can find the sample variance by dividing the sum of squares by n − 1 and the sample standard deviation by finding the square root of the sample variance. (a) Show how to obtain the alternative formula. (b) Use the alternative formula to calculate the sample standard deviation for the data set in Exercise 15. (c) Compare your result with the sample standard deviation obtained in Exercise 15.
Solution Summary: The author explains how to obtain the alternative formula for calculating the variance and standard deviation.
Alternative Formula You used
S
S
x
=
Σ
(
x
−
x
¯
)
2
when calculating variance and standard deviation. An alternative formula that is sometimes more convenient for hand calculations is
S
S
x
=
Σ
x
2
−
(
Σ
x
)
2
n
.
You can find the sample variance by dividing the sum of squares by n − 1 and the sample standard deviation by finding the square root of the sample variance.
(a) Show how to obtain the alternative formula.
(b) Use the alternative formula to calculate the sample standard deviation for the data set in Exercise 15.
(c) Compare your result with the sample standard deviation obtained in Exercise 15.
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Chapter 2 Solutions
Elementary Statistics: Picturing the World Books a la carte Plus MyLab Statistics with Pearson eText -- Access Card Package (7th Edition)
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