MATH 1131 3.0  Fall 2011
Solution for Assignment 1
Question 1:
a)
The 5number summary from MINITAB are:
Male:
410.00
490.75
504.50
527.00
554.00
Female:
401.00
480.50
494.00
514.00
543.00
Using R, we have
Male:
410.0
493.8
504.5
526.2
554.0
Female:
401.0
482.8
494.0
513.0
543.0
Using hand calculation, we have
Male:
Q1 is between 484 and 493, Median is between 504 and 505, and
Q3 is between 527 and 527
Therefore the 5number summary is:
410.0
488.5
504.5
527.0
554.0
Female:
Q1 is between 476 and 482, Median is between 494 and 494, and
Q3 is between 513 and 517
Therefore the 5number summary is:
410.0
479.0
494.0
515.0
543.0
Any of the above answer is acceptable.
b)
Many graphical presentations are and the following is the backtoback stemplot
(Leaf Unit = 1):
Female
Stem
Male
1
40
41
0
1
42
7
43
44
973
45
46
2
60
47
049
77652
48
4
64421
49
36899
8840
50
03457
7733
51
3478
034
52
477
53
3467
54
55
24
The distributions of males’s scores and females’ scores have more or less the
same shape (skewed with a long left tail).
The six highest scores are from males
and the lowest score is from female.
However, the difference in scores does not
seem like it is a big difference.
I will say that they have very similar
performances.
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We can use the sidebyside boxplots.
Females
Males
560
540
520
500
480
460
440
420
400
Data
Boxplot of Males, Females
From the plot, the performances are more or less the same (even though females’
scores seem to be slightly lower than males’ score, but they are not significantly
lower because the boxes overlapped).
c)
Since the distribution of males’ scores does not look like it is bellshaped, we will
be using the inner fences and outer fences to determine if outliers exist or not.
I
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 Fall '10
 Wong
 Math, Statistics, Standard Deviation, 5number summary

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