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# Percentiles and Quartiles

1.
Grades: Test scores: Clayton and timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy?

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Problem #2
Sociology High school dropouts;
What percentage of the general u.s. population are high school dropouts: the statistical abstract of the United States 120th edition, give the percentage of high school dropouts by state. For convenience, the data are sorted in increasing order.

5 6 7 7 7 7 8 8 8 8
8 9 9 9 9 9 9 9 10 10
10 10 10 10 10 10 11 11 11 11
11 11 11 11 12 12 12 12 13 13
13 13 13 13 14 14 14 14 14 15

Make a box and whisker plot and find the interquartile range.

Wyoming has a dropout rate of about 7%. Into what quartile does this rate fall?

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Problem #3
Outliers
Lower limit Q1 - 1.5 x (1QR)
Upper limit Q3 + 1.5 x (1QR)

Students from a statistics class were asked to record their heights in inches, the heights are as follows
65 72 68 64 60 55 73 71 52 63 61 74
69 67 74 50 4 75 67 62 66 80 64 65

Make a box and whisker plot of the data
Find the value of the interquartile range (1QR)
Multiply the 1QR by 1.5 and find the lower and upper limits.
Are thee any data values below the lower limit: above the upper limit?
List any suspected outliers. What might be some explanations for the outliers:

#### Solution Preview

Hi I have 3 different statistics problems I do okay but do not have my calculator and I keep missing a step when doing it by hand. Please help!

1.
Grades: Test scores: Clayton and timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain. Obvious Timothy ranked better but I cannot explain these please help. Thank you

Even though Clayton has a better raw score than Timothy (85 vs 83), Timothy performed better with respect to the rest of his class. Timothy scored better than 72% of the other students, while Clayton only scored better than 70% of the students.

This is a way to compare test performance when the exams aren't the same. For instance, maybe Clayton's exam ...

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