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Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

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SECTION 2.4 | Percentiles, Percentile Ranks, and Interpolation 55

A percentage value of 40% is not given in the table; however, it is located between 10%

and 60%, which are given. These two percentage values are associated with the upper real

limits of 4.5 and 9.5, respectively. These values are shown in the following table:

Scores (X)

Percentages

Top 9.5 60%

? 40% Intermediate value

Bottom 4.5 10%

STEP 1

STEP 2

STEP 3

For the scores, the width of the interval is 5 points. For the percentages, the width is

50 points.

The value of 40% is located 20 points from the top of the percentage interval. As a fraction

of the whole interval, this is 20 out of 50, or 2 5 of the total interval.

Using this same fraction for the scores, we obtain a distance of

2

(5 points) = 2 points

5

The location we want is 2 points down from the top of the score interval.

STEP 4

Because the top of the interval is 9.5, the position we want is

9.5 – 2 = 7.5

This is the answer. The 40 th percentile is X = 7.5.

The following example is an opportunity for you to test your understanding by doing

interpolation yourself.

EXAMPLE 2.10

Using the frequency distribution table in Example 2.9, use interpolation to find the percentile

rank for X = 9.0. You should obtain 55%. Good luck.

LEARNING CHECK

1. In a distribution of exam scores, which of the following would be the highest score?

a. the 20 th percentile

b. the 80 th percentile

c. a score with a percentile rank of 15%

d. a score with a percentile rank of 75%

2. Following are three rows from a frequency distribution table. For this distribution,

what is the 90th percentile?

a. X = 24.5

b. X = 25

c. X = 29

d. X = 29.5

X c%

30–34 100%

25–29 90%

20–24 60%

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