Statistical Exercises

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Statistical Exercises

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Answer 1
a. Mean = 1561
Median = 1542.5
80 percentile SAT score = 1760
Table 1: Frequency distribution of SAT scores
Figure 1: Histogram of SAT scores for all students
b. For Ampipe school students
Mean = 1499.33
Median = 1485
80 percentile SAT score = 1684

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Table 2: Frequency distribution of SAT scores of Ampipe School
CLASS LL UL MID FREQUENCY
1001-1200 1000.5 1200.5 1100.5 1
1201-1400 1200.5 1400.5 1300.5 4
1401-1600 1400.5 1600.5 1500.5 5
1601-1800 1600.5 1800.5 1700.5 5
Figure 2: Histogram of SAT scores for all students of Ampipe School
c. For Walnut Heights school students
Mean = 1622.67
Median = 1585
80 percentile SAT score = 1920
Table 3: Frequency distribution of SAT scores of Walnut Heights School

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Figure 3: Histogram of SAT scores for all students of Walnut Heights School
d. For Ampipe School
N = 15
(SAT>1400) =10
P (SAT>1400)= 10/15 = 0.667
For Walnut Heights School
N = 15
(SAT>1400) = 11
P (SAT>1400) = 11/15 = 0.733
SAT score was not independent of school, and rather a marked difference in distribution
of SAT scores was observed between the two schools. Scores were higher in Walnut
Heights School compared to Ampipe School, due to existence of few unusual higher
SAT marks in Walnut Heights.