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Scores on the final in a statistics class are as follows.
75  25  75  52  80  85  80  99  90  60 
86  92  40  74  72  55  87  70  85  70 
a. Calculate the 25th, 50th, and 75th percentiles. (Use the methodology shown in Section 3.2 of the text to calculate the percentiles. Do not round intermediate calculations. Round your answers to 2 decimal places.)

The director of
graduate admissions at a local university is analyzing the
relationship between scores on the Graduate Record Examination
(GRE) and subsequent performance in graduate school, as measured by
a student’s grade point average (GPA). She uses a sample of 10
students who graduated within the past five years.
GRE  GPA 
1500  3.4 
1400  3.5 
1000  3.0 
1050  2.9 
1100  3.0 
1250  3.3 
800  2.7 
850  2.8 
950  3.2 
1350  3.3 
a1. Calculate the covariance. (Round your answer to 2 decimal places.)

a2. Interpret the covariance.

b1. Calculate the coefficient of correlation. (Round your answer to 2 decimal places.)

b2. Does an applicant’s GRE score seem to be a
good indicator of subsequent performance in graduate
school?
Yes
No
a)
applying above score in an ascending order:
s, no  X 
1  25 
2  40 
3  52 
4  55 
5  60 
6  70 
7  70 
8  72 
9  74 
10  75 
11  75 
12  80 
13  80 
14  85 
15  85 
16  86 
17  87 
18  90 
19  92 
20  99 
25 th percentile =(n+1)/4 th value =5.25 th value =60+0.25*(7060)=62.5
50th percentile =(n+1)/2 th value =10.5 th value =75
75 th percentile =3(n+1)/4 th value =15.75 th value =85+0.75*(8685)=85.75
a1) covariance=57.50
a2) There is positive relationship between GRE and GPA.
a3) correlation =0.89
b2) Yes (as correlation coefficient is significantly high)
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