Four Questions: Savings Rate, Tax, Wonderlic and Compensation

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(3.31, 3.39, 3.49, 3.73)

The file SavingRate contains the yields for a money market account, a one-year certificate of deposit (CD), and a five-year CD for 23 banks in the metropolitan New York area, as of May 28, 2009. For each type of account:
a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range.
b. List the five -number summary.
c. Construct a boxplot and describe the shape.
a)First, we arrange the data in order for the one year certificate of deposite:
0.25
0.75
0.85
1.00
1.20
1.35
1.50
1.65
1.75
1.75
1.75
2.00
2.00
2.00
2.00
2.00
2.00
2.05
2.10
2.20
2.24
2.25
2.30
Q2=12th data=2.00
Q1=(6th data+7th data)/2=(1.35+1.50)/2=1.425
Q3=(17th data+18th data)/2=(2.00+2.05)/2=2.025
Interquartile range=Q3-Q1=2.025-1.425=0.60
b)Five number summary: 0.25, 1.425, 2.00, 2.025, 2.30
0.25 is an outlier since 0.25<1.425-1.5*0.60=0.525
a')first, we arrange the data in order for five year CD:
1.00
1.16
1.50
1.65
1.70
1.70
1.70
1.70
1.85
2.50
2.80
3.00
3.00
3.00
3.10
3.25
3.25
3.30
3.30
3.30
3.50
3.66
3.70
Q2=12th data=3.00
Q1=(6th data+7th data)/2=(1.70+1.70)/2=1.70
Q3=(17th data+18th data)/2=(3.25+3.30)/2=3.275
Interquartile range=Q3-Q1=3.275-1.70=1.575
b'. the five number summary is: 1.00, 1.70, 3.00, 3.275, 3.70.
c)we could have box plot for both 1 year and 5 year CD.

From the box plot, we could see that both distribution is skewed to the left.
The file Tax contains the quarterly sales tax receipts (in thousands of dollars ) submitted to the comptroller of the Village of Fair Lake for the period ending March 2009 by all 50 businesses established in the locale:
10.3 11.1 9.6 9.0 14.5
13.0 6.7 11.0 8.4 10.3
8.0 11.8 8.7 10.6 9.5
11.1 10.2 11.1 9.9 9.8
11.6 15.1 12.5 6.5 7.5
10.0 12.9 9.2 10.0 12.8
12.5 9.3 10.4 12.7 10.5
9.3 11.5 10.7 11.6 7.8
10.5 7.6 10.1 8.9 8.6
a. Compute the mean, variance, and standard deviation for this population
b. What percentage of these businesses have quarterly sales tax receipts within + 1, + 2, or + 3
standard deviations of the mean?
c. Compare your findings with what would be expected on the basis of the empirical rule. Are you surprised at the results in (b).
a. mean=(10.3+11.1+...+8.6)/50=10.28
since this is a population, variance=((10.3-10.28)^2+(11.1-10.28)^2+...+(8.6-10.28)^2)/50=4.0984
standard deviation=sqrt(4.0984)= 2.024451
b. within 1 standard deviation: from 8.256 to 12.304. there are 32 data within this range. Therefore, The percentage: 32/50=64%.
Within 2 standard deviation: from 6.231 to 14.329. there are 47 data within this range. Therefore, the percentage: 47/50=94%
Within 3 ...