Question

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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.)

25th percentile
50th percentile	75.00
75th percentile

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

a-1. Calculate the covariance. (Round your answer to 2 decimal places.)

Covariance

a-2. Interpret the covariance.

There is

relationship between GRE and GPA.

b-1. Calculate the coefficient of correlation. (Round your answer to 2 decimal places.)

Coefficient of correlation

b-2. Does an applicant’s GRE score seem to be a good indicator of subsequent performance in graduate school?

Yes

No

Answer 1

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*(70-60)=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*(86-85)=85.75

a-1) covariance=57.50

a-2) There is positive relationship between GRE and GPA.

a-3) correlation =0.89

b-2) Yes (as correlation coefficient is significantly high)