7. Obtain the following summaries for Miles and Miles_1. [Go to stat, Summary St
ID: 3070163 • Letter: 7
Question
7. Obtain the following summaries for Miles and Miles_1.
[Go to stat, Summary Stats, Columns, Select columns, choose Statistics, Compute.]
Variable
N
Mean
Std
Median
Q1
Q3
Min
Max
Range
IQR
Miles
Miles_1
Note you should notice that Mean ‘Miles’ is much larger than the Mean ‘Miles_1’, and Median ‘Miles’ is similar to ‘Median ‘Miles_1’. This justifies your results in Q3.
(a) Compute an estimate of standard deviation, s, for Miles_1 using Range/6 = _______________.
How close is this estimated s to the actual standard deviation of Miles_1:
Estimate s.d./Actual s.d. = _____________
Suppose a student has the Distance of 40. Use the Empirical rule based on the information of ‘Miles_1 variable to decide if this is an unusual Distance or not.
[Note: since the distribution of Miles_1 is not mounded-shaped, Empirical Rule does not work well. However, we can use Empirical rule to identify unusual cases.]
(e) Suppose a student has the Distance of 300. Compute the corresponding Z-score and using the Empirical rule to decide if this is an unusually far distance away from home or not.
Variable
N
Mean
Std
Median
Q1
Q3
Min
Max
Range
IQR
Miles
Miles_1
Explanation / Answer
Answer:
### First sorting the data of Miles for Male and female in excel:
### By using R command:
> MilesMale=c(72,100,125,200,65,170,120,375,10,62,151,132,20,328,9000,40,200,100,150,103,143,140,136,4.1,8,200,140,65,137,140,10,8.7,200,50,120,2,133,125,163,90,45,160,100,50,115,30,40,0,2100,8,19,85,145,50,145,155,120,160,130,170,5,120,70,996,80,155,50,55,150,112,168,125,9999.99,113,120,2184,25,22,150,73,65,100,90,9000,110,155,20,5,61,132,130,120,45,35,110,120,8,1250,40,65,12,160,130,130,130,154,100,280,121,150,5,65,155,30,100,60,100,90,100,75)
> MilesMale
[1] 72.00 100.00 125.00 200.00 65.00 170.00 120.00 375.00 10.00
[10] 62.00 151.00 132.00 20.00 328.00 9000.00 40.00 200.00 100.00
[19] 150.00 103.00 143.00 140.00 136.00 4.10 8.00 200.00 140.00
[28] 65.00 137.00 140.00 10.00 8.70 200.00 50.00 120.00 2.00
[37] 133.00 125.00 163.00 90.00 45.00 160.00 100.00 50.00 115.00
[46] 30.00 40.00 0.00 2100.00 8.00 19.00 85.00 145.00 50.00
[55] 145.00 155.00 120.00 160.00 130.00 170.00 5.00 120.00 70.00
[64] 996.00 80.00 155.00 50.00 55.00 150.00 112.00 168.00 125.00
[73] 9999.99 113.00 120.00 2184.00 25.00 22.00 150.00 73.00 65.00
[82] 100.00 90.00 9000.00 110.00 155.00 20.00 5.00 61.00 132.00
[91] 130.00 120.00 45.00 35.00 110.00 120.00 8.00 1250.00 40.00
[100] 65.00 12.00 160.00 130.00 130.00 130.00 154.00 100.00 280.00
[109] 121.00 150.00 5.00 65.00 155.00 30.00 100.00 60.00 100.00
[118] 90.00 100.00 75.00
> summary(MilesMale)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 53.75 112.50 382.88 150.00 9999.99
> n1=length(MilesMale)
> n1
[1] 120
> IQR=150-53.75
> IQR
[1] 96.25
> MileFemale=c(140,57,275,123,150,20,142,200,41.6,200,33,130,180,100,210,550,171,130,100,150,56,170,150,139,45,125,110,60,72,9999.99,15,125,0,120,150,86.8,105,8000,124,70,80,150,160,67.7,153,55,2,3,30,238,45,15,1.5,12,140,47,85,110,100,110,105,122,250,6,150,60,93,26,160,150,2,0,63,160,143,85,50,15,1490)
> MileFemale
[1] 140.00 57.00 275.00 123.00 150.00 20.00 142.00 200.00 41.60
[10] 200.00 33.00 130.00 180.00 100.00 210.00 550.00 171.00 130.00
[19] 100.00 150.00 56.00 170.00 150.00 139.00 45.00 125.00 110.00
[28] 60.00 72.00 9999.99 15.00 125.00 0.00 120.00 150.00 86.80
[37] 105.00 8000.00 124.00 70.00 80.00 150.00 160.00 67.70 153.00
[46] 55.00 2.00 3.00 30.00 238.00 45.00 15.00 1.50 12.00
[55] 140.00 47.00 85.00 110.00 100.00 110.00 105.00 122.00 250.00
[64] 6.00 150.00 60.00 93.00 26.00 160.00 150.00 2.00 0.00
[73] 63.00 160.00 143.00 85.00 50.00 15.00 1490.00
> n2=length(MileFemale)###Sample size
> n2
[1] 79
> summary(MileFemale)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 52.5 110.0 348.9 150.0 10000.0
> IQR
[1] 96.25
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.